Statistics

Anonymous
timer Asked: Jun 29th, 2018
account_balance_wallet $20

Question description

quiz 44 questions

    1. Solve for probabilities in a continuous uniform distribution
    2. Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve
    3. Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity



    1. Solve for probabilities in a continuous uniform distribution
    2. Solve for probabilities in a normal distribution using z scores and for the mean, the standard deviation, or a value of x in a normal distribution when given information about the area under the normal curve
    3. Solve problems from the discrete binomial distribution using the continuous normal distribution and correcting for continuity

QUESTION 1 1. The weight of softballs is uniformly distributed over the interval of 8 to 12 ounces, inclusively. What is the probability that a randomly selected softball will weigh between 13 and 15 ounces? 0.250 0.500 0.375 0.000 1.000 QUESTION 2 1. If the weight of softballs is uniformly distributed over the interval of 8 to 12 ounces, inclusively then what is the probability that a randomly selected softball will weigh more than 10 ounces? 0.750 0.000 0.333 0.500 0.900 QUESTION 3 1. The time it takes (in minutes) to change a flat tire is uniformly distributed. The time is distributed over a uniform interval of 20 to 30 minutes, inclusively. What is the probability that the change of a flat tire will be completed in 21.75 to 24.25 minutes? 0.250 0.333 0.375 0.000 1.000 QUESTION 4 Z is a normally distributed random variable. The distribution of Z has a mean equal to 0 and a standard deviation equal to 1. What is the probability that z will be less than 1.3 or P(Z <1.3) ? 0.4032 0.9032 0.0968 0.3485 0. 5485 QUESTION 5 If Z is a normally distributed random variable with a mean equal to 0 and a standard deviation of 1, what is the probability that Z will be greater than -1.1 or P(Z > -1.1)? 0.36432 0.8643 0.1357 -0.1357 -0.8643 QUESTION 6 The number of miles a Ford Explorer is driven before needing a major repair is known to be normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles. What is the probability that a randomly selected Explorer will travel at least 50,000 miles before needing a major repair? 0.0228 0.9772 0.5000 0.4772 1.0000 QUESTION 7 1. The net gain on an investment in gold is normally distributed with a mean of $10,000 and a standard deviation of $5,000. What is the probability that an investor will realize a net gain of at least $5,000 on his investment in gold? 0.1859 0.3413 0.8413 0.4967 0.5000 QUESTION 8 1. The diameter of flex piping used in commercial heating systems is normally distributed with a mean of 30.5 inches and a standard deviation of 0.20 inches. What is the probability that a randomly selected section of flex pipe will have a diameter of less than 31 inches? 0.00 0.9938 .8289 .5987 QUESTION 9 1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces of juice? .0475 .4525 .9525 .9554 QUESTION 10 1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.What is the probability that a randomly selected apple will contain between 2.00 and 2.15 ounces? .4525 .2039 .2486 .7011 QUESTION 11 1. The organizers of the "Holy Smokes Marathon" provide bottled water to the participants and spectators during the race. Based on data collected in the past, the organizers know that the number of bottles of water passed out is normally distributed with a mean of 200 bottles and a standard deviation of 20 bottles. Based on this information, what is the probability that at this year's race they will hand out between 180 and 210 bottles of water? .6915 .1915 .5328 .1587 QUESTION 12 1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is randomly selected, what is the probability that his or her starting salary will be at least $30,000? 0.4772 0.9772 0.0228 0.5000 QUESTION 13 1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is randomly selected, what is the probability that his or her starting salary will be at least $47,500? 0.4332 0.9332 0.0668 0.5000 QUESTION 14 1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is randomly selected, what is the probability that his or her starting salary will be between $34,000 and $46,000? 38.49% 38.59% 50% 76.98% QUESTION 15 1. When a z-score is calculated and the result is a negative value, this indicates that ______________. the value of X used to calculate the z score is located to the right of the mean. the value of X used to calculate the z score is located to the left of the mean. an error was made when calculating the z score since a z score cannot be negative the value of the mean of the distribution is negative. QUESTION 16 The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months? 500,000 808,500 308,500 191,500 QUESTION 17 Which of the following is not a characteristic of the normal probability distribution? The mean, median, and the mode are equal The mean of the distribution can be negative, zero, or positive The distribution is symmetrical The standard deviation must be 1 QUESTION 18 The weight of pallets of sod is known to be normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a pallet is randomly selected, what is the probability that it weighs more than 241.25 pounds? 0.4505 0.0495 0.9505 0.9010 QUESTION 19 The weight of pallets of sod is known to be normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a pallet is randomly selected, what is the probability that it weighs less than 250 pounds? 0.4772 0.9772 0.0528 0.5000 QUESTION 20 The weight of pallets of sod is known to be normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a pallet is randomly selected, what is the probability that it weighs between 180 and 215 pounds? 28.81% 6.24% 22.57% 51.38% QUESTION 21 1. The length of time that customers spend waiting in the drive-through impacts overall customer satisfaction accordingto a recent survey conducted by the National Association of Fast Food Restaurants. As a result, Speedy Burger is launching a promotion that awards customers who wait "too long" a voucher for a free Speedy Meal. Management is committed to the promotion, but is concerned about how many Speedy Meals that could potentially give away, thereby reducing their profits. If Speedy Burger wants to give away free meals to no more than 1% of its drive-through customers, what is the maximum wait time before a free meal is awarded if it is know that the average wait time is 138.5 seconds with a standard deviation of 29 seconds? 139 seconds 153 seconds 71 seconds 206 seconds QUESTION 22 1. The number of rushing yards per game for the top running backs in the NFL is approximately normally distributed. On average, these elite players rush for 266 yards per game. In fact, according to data collected these players rushed for fewer than 244 yards only 0.46% of the time. Based on this information, what is the value of the standard deviation for the distribution of rushing yards? 122 yards 16 yards 44 yards 8.4 yards QUESTION 23 1. The length of time it takes to change a light bulb is normally distributed with a mean of 60 seconds and a standard deviation of 2 seconds. If the length of time that it takes Candy to change the light bulb in the lamp next her bed table falls1.3 standard deviations below the mean, how long did it take her? 58.7 seconds 61.3 seconds 62.6 seconds 57.4 seconds 54.7 QUESTION 24 1. Tick-Tock manufacturing has determined it can afford to pay a longevity bonus to employees based on their years of service with the company. They have determined that on average employees have been with the company for 4 years. Employee longevity is normally distributed and has a standard deviation of eight months. If they only want to give bonuses to 5% of Tick-Tock employees, what is the minimum number of months an employee will have to have been at the company in order to receive this bonus? 32.82 months 61.16 months 34.84 months 42.67 months QUESTION 25 1. Your broker calls you with information about an investment opportunity. He informs you that the net profits from this investment are normally distributed and on average the net profit is $10,000. He urges you to make the investment since the standard deviation of the profits is $5,000. Based on this information, what is the probability that you will at least break even on the investment and not suffer a loss? 47.72% 2.28% 95.44% 97.72% 100% QUESTION 26 1. The weight of sandbags used to protect against flooding is normally distributed with a mean weight of 74 pounds and a standard deviation of 10 pounds. A sandbag is considered to be too light to be effective if it weighs less than 54 pounds. Concerned about the consequences of sandbags failing to hold back flood waters, a disaster prep team decides to weigh all of the bags on the next delivery truck. They weigh the bags and find that 8 are underweight. Approximately how many sandbags were in the delivery? 350 285 200 2700 QUESTION 27 1. The weight of a "mini" candy bar is normally distributed with a standard deviation of 0.50 ounces. The production manager wants no more than 5% of the individual candy bars to weigh in excess of 5.1 ounces. What should he establish as the average weight in order for production to meet this specification? 4.278 ounces 4.409 ounces 3.455 ounces 5.922 ounces QUESTION 28 1. The average monthly rent for apartments in midtown Manhattan are normally distributed with a mean of $4,000. According to a local real estate firm, only 1.7% of the apartments in midtown Manhattan rent for less than $2,834 per month. Based on this information, what is the value of the standard deviation of the monthly rents for apartments in midtown Manhattan? $5.50 $1,166 $550 $48.18 QUESTION 29 1. Research was conducted regarding "in app" purchases associated with online games like Candy Crush and Clash of Clans. The research showed that gamers spent an average of $8.22 on "in app" purchases associated with a game in the previous 30 days. The expenditures were approximately normally distributed with a standard deviation of $1.10. Based on this information, 80% of the gamers spent more than what amount on "in app" purchases? $7.30 $7.38 $9.06 $9.14 QUESTION 30 1. A manufacturer of energy efficient LED light bulbs tests competing brands and finds that the amounts of energy they require is normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. In order to get a more realistic picture of the amount of energy their competitors' light bulbs are actually using they decide to run a second set of tests. However, the lowest 25% and the highest 35% are not going to be included in the next round of tests. Based on this, what are the upper and lower limits for the energy usage of the light bulbs that will be included in the second round of testing? [269.76 300.24] [278.90, 288.55] [280.22 289.78] [280.22 300.24] QUESTION 31 1. To be accepted to the veterinarian school at State University, applicants must have an entrance exam score within the 95th percentile. If the average score on the entrance exam is 1000 and the exam has a standard deviation of 200, what is the lowest possible score a student needs in order to be accepted to the program if the scores are normally distributed? 1400 1330 1250 1100 QUESTION 32 1. The starting salary for employees at We-B-Burgers are normally distributed with a standard deviation of $5,000. If the mean salary of these employees is $25,000 per year and sixty-eight of them earn more than $35,600 per year how many people are employed by We-B-Burgers? 4,000 2,500 2,000 4,100 QUESTION 33 1. Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally with a mean of 30 minutes and a standard deviation of 8 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15% of the customers should receive this discount. What are the numbers of minutes they need to wait to receive the discount? 34.48 minutes 21.68 minutes 25.52 minutes 38.31 minutes QUESTION 34 1. Suppose the distribution of personal daily water usage in New York City is normally distributed with a mean of 15 gallons and a variance of 25 gallons. Because of a current problem with the distribution of water to its citizens, the mayor wants to give a city tax rebate to the 15 percent of the population who use the least amount of water. What should he use as the water limit for a person to qualify for a city tax rebate? 15.00 gallons 12.20 gallons 9.83 gallons 10.25 gallons QUESTION 35 1. The average time a worker spends on the Internet looking at their personal social media accounts during business hours is 49 minutes per day. Assume the standard deviation is 16 minutes and that the times are normally distributed. For the 10% who spend the most time looking at their personal social media accounts during business hours, how much time do they spend? 28.52 minutes 69.48 minutes 86.28 minutes 11.72 minutes QUESTION 36 1. In grading eggs into small, medium, and large, the Nancy Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal. The value of the mean is and the value of the standard deviation is QUESTION 17 1. The weekly earnings of bus drivers are normally distributed with a mean of $395. If only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers? QUESTION 38 1. Gilligan Boatworks has received more warranty claims this year associated with cracking in the exterior finish of the hull. Gel coat that is too thin negatively affects the finish over the life of the boat because of exposure to salt water and sunlight, so Gilligan wants to start his failure analysis with gel coat. He gets his production supervisor to collect data about the gel coat process and it is determined that the average thickness of the coating is 15mm with a standard deviation of 2.5mm. In order to ensure that no more than 2.5% of the hulls are "too thin" what is the minimum thickness of the gel coat? 19.9mm 10.1mm 13.8mm 14.9mm QUESTION 39 1. The average life expectancy of the Big Daddy air compressor is 6 years with a standard deviation of 8 months. Assume that the lives of the air compressors are normally distributed. If 155 of this year's air compressor production fail to operate properly in less than 4 years and 4 months, how many air compressors were produced this year? 25,000 314 250 2,536 QUESTION 40 1. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? 90.51 93.2 88.51 100.00 QUESTION 41 1. A national survey conducted in 2017 asked employed adults from age 25 to 70 if they plan to keep a foot in the working world after retirement. Thirty-three percent of the respondents answered "very likely". A random sample of 75 adults from this age group was asked the same question. Using the normal approximation to the binomial distribution, what is the probability that more than 18 adults from this sample would "very likely" plan to keep a foot in the working world after retirement? 0.9370 0.6772 0.8413 0.5557 QUESTION 42 1. According to the National Movie Theater Owners Association, 26.0% of movie goers sneak candy and drinks into the theater to avoid the high prices at the concession stand. A random sample of 90 movie goers was taken and they were asked whether they had ever "snuck" candy or drinks into the theater to avoid the high prices at the concession stand. Using the normal approximation to the binomial distribution, what is the probability that fewer than 19 people from this sample said they had? 0.1190 0.2530 0.4149 0.3879 QUESTION 43 1. Tropical Sun, a new brand of suntan lotions is determining whether their new scent, "Wet Sand" will appeal to beach goers. A national survey determined that 33% of people found the smell appealing, and they were encouraged by these results. They are now conducting their own survey and randomly sample 75 people and ask them if the new scent is appealing. What is the probability that between 20 and 23 people will say that they find the scent appealing. Use the normal approximation to the binomial when solving for the probability. 0.1510 0.4560 0.278 0.6539 QUESTION 44 The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500. a. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor's? b.Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? c. What are the minimum and the maximum incomes of the middle 95% of the residents? d.Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City
QUESTION 1 1. The weight of softballs is uniformly distributed over the interval of 8 to 12 ounces, inclusively. What is the probability that a randomly selected softball will weigh between 13 and 15 ounces? 0.250 0.500 0.375 0.000 1.000 QUESTION 2 1. If the weight of softballs is uniformly distributed over the interval of 8 to 12 ounces, inclusively then what is the probability that a randomly selected softball will weigh more than 10 ounces? 0.750 0.000 0.333 0.500 0.900 QUESTION 3 1. The time it takes (in minutes) to change a flat tire is uniformly distributed. The time is distributed over a uniform interval of 20 to 30 minutes, inclusively. What is the probability that the change of a flat tire will be completed in 21.75 to 24.25 minutes? 0.250 0.333 0.375 0.000 1.000 QUESTION 4 Z is a normally distributed random variable. The distribution of Z has a mean equal to 0 and a standard deviation equal to 1. What is the probability that z will be less than 1.3 or P(Z <1.3) ? 0.4032 0.9032 0.0968 0.3485 0. 5485 QUESTION 5 If Z is a normally distributed random variable with a mean equal to 0 and a standard deviation of 1, what is the probability that Z will be greater than -1.1 or P(Z > -1.1)? 0.36432 0.8643 0.1357 -0.1357 -0.8643 QUESTION 6 The number of miles a Ford Explorer is driven before needing a major repair is known to be normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles. What is the probability that a randomly selected Explorer will travel at least 50,000 miles before needing a major repair? 0.0228 0.9772 0.5000 0.4772 1.0000 QUESTION 7 1. The net gain on an investment in gold is normally distributed with a mean of $10,000 and a standard deviation of $5,000. What is the probability that an investor will realize a net gain of at least $5,000 on his investment in gold? 0.1859 0.3413 0.8413 0.4967 0.5000 QUESTION 8 1. The diameter of flex piping used in commercial heating systems is normally distributed with a mean of 30.5 inches and a standard deviation of 0.20 inches. What is the probability that a randomly selected section of flex pipe will have a diameter of less than 31 inches? 0.00 0.9938 .8289 .5987 QUESTION 9 1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces of juice? .0475 .4525 .9525 .9554 QUESTION 10 1. An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.What is the probability that a randomly selected apple will contain between 2.00 and 2.15 ounces? .4525 .2039 .2486 .7011 QUESTION 11 1. The organizers of the "Holy Smokes Marathon" provide bottled water to the participants and spectators during the race. Based on data collected in the past, the organizers know that the number of bottles of water passed out is normally distributed with a mean of 200 bottles and a standard deviation of 20 bottles. Based on this information, what is the probability that at this year's race they will hand out between 180 and 210 bottles of water? .6915 .1915 .5328 .1587 QUESTION 12 1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is randomly selected, what is the probability that his or her starting salary will be at least $30,000? 0.4772 0.9772 0.0228 0.5000 QUESTION 13 1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is randomly selected, what is the probability that his or her starting salary will be at least $47,500? 0.4332 0.9332 0.0668 0.5000 QUESTION 14 1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is randomly selected, what is the probability that his or her starting salary will be between $34,000 and $46,000? 38.49% 38.59% 50% 76.98% QUESTION 15 1. When a z-score is calculated and the result is a negative value, this indicates that ______________. the value of X used to calculate the z score is located to the right of the mean. the value of X used to calculate the z score is located to the left of the mean. an error was made when calculating the z score since a z score cannot be negative the value of the mean of the distribution is negative. QUESTION 16 The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months? 500,000 808,500 308,500 191,500 QUESTION 17 Which of the following is not a characteristic of the normal probability distribution? The mean, median, and the mode are equal The mean of the distribution can be negative, zero, or positive The distribution is symmetrical The standard deviation must be 1 QUESTION 18 The weight of pallets of sod is known to be normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a pallet is randomly selected, what is the probability that it weighs more than 241.25 pounds? 0.4505 0.0495 0.9505 0.9010 QUESTION 19 The weight of pallets of sod is known to be normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a pallet is randomly selected, what is the probability that it weighs less than 250 pounds? 0.4772 0.9772 0.0528 0.5000 QUESTION 20 The weight of pallets of sod is known to be normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. If a pallet is randomly selected, what is the probability that it weighs between 180 and 215 pounds? 28.81% 6.24% 22.57% 51.38% QUESTION 21 1. The length of time that customers spend waiting in the drive-through impacts overall customer satisfaction accordingto a recent survey conducted by the National Association of Fast Food Restaurants. As a result, Speedy Burger is launching a promotion that awards customers who wait "too long" a voucher for a free Speedy Meal. Management is committed to the promotion, but is concerned about how many Speedy Meals that could potentially give away, thereby reducing their profits. If Speedy Burger wants to give away free meals to no more than 1% of its drive-through customers, what is the maximum wait time before a free meal is awarded if it is know that the average wait time is 138.5 seconds with a standard deviation of 29 seconds? 139 seconds 153 seconds 71 seconds 206 seconds QUESTION 22 1. The number of rushing yards per game for the top running backs in the NFL is approximately normally distributed. On average, these elite players rush for 266 yards per game. In fact, according to data collected these players rushed for fewer than 244 yards only 0.46% of the time. Based on this information, what is the value of the standard deviation for the distribution of rushing yards? 122 yards 16 yards 44 yards 8.4 yards QUESTION 23 1. The length of time it takes to change a light bulb is normally distributed with a mean of 60 seconds and a standard deviation of 2 seconds. If the length of time that it takes Candy to change the light bulb in the lamp next her bed table falls1.3 standard deviations below the mean, how long did it take her? 58.7 seconds 61.3 seconds 62.6 seconds 57.4 seconds 54.7 QUESTION 24 1. Tick-Tock manufacturing has determined it can afford to pay a longevity bonus to employees based on their years of service with the company. They have determined that on average employees have been with the company for 4 years. Employee longevity is normally distributed and has a standard deviation of eight months. If they only want to give bonuses to 5% of Tick-Tock employees, what is the minimum number of months an employee will have to have been at the company in order to receive this bonus? 32.82 months 61.16 months 34.84 months 42.67 months QUESTION 25 1. Your broker calls you with information about an investment opportunity. He informs you that the net profits from this investment are normally distributed and on average the net profit is $10,000. He urges you to make the investment since the standard deviation of the profits is $5,000. Based on this information, what is the probability that you will at least break even on the investment and not suffer a loss? 47.72% 2.28% 95.44% 97.72% 100% QUESTION 26 1. The weight of sandbags used to protect against flooding is normally distributed with a mean weight of 74 pounds and a standard deviation of 10 pounds. A sandbag is considered to be too light to be effective if it weighs less than 54 pounds. Concerned about the consequences of sandbags failing to hold back flood waters, a disaster prep team decides to weigh all of the bags on the next delivery truck. They weigh the bags and find that 8 are underweight. Approximately how many sandbags were in the delivery? 350 285 200 2700 QUESTION 27 1. The weight of a "mini" candy bar is normally distributed with a standard deviation of 0.50 ounces. The production manager wants no more than 5% of the individual candy bars to weigh in excess of 5.1 ounces. What should he establish as the average weight in order for production to meet this specification? 4.278 ounces 4.409 ounces 3.455 ounces 5.922 ounces QUESTION 28 1. The average monthly rent for apartments in midtown Manhattan are normally distributed with a mean of $4,000. According to a local real estate firm, only 1.7% of the apartments in midtown Manhattan rent for less than $2,834 per month. Based on this information, what is the value of the standard deviation of the monthly rents for apartments in midtown Manhattan? $5.50 $1,166 $550 $48.18 QUESTION 29 1. Research was conducted regarding "in app" purchases associated with online games like Candy Crush and Clash of Clans. The research showed that gamers spent an average of $8.22 on "in app" purchases associated with a game in the previous 30 days. The expenditures were approximately normally distributed with a standard deviation of $1.10. Based on this information, 80% of the gamers spent more than what amount on "in app" purchases? $7.30 $7.38 $9.06 $9.14 QUESTION 30 1. A manufacturer of energy efficient LED light bulbs tests competing brands and finds that the amounts of energy they require is normally distributed with a mean of 285 kwh and a standard deviation of 9.1 kwh. In order to get a more realistic picture of the amount of energy their competitors' light bulbs are actually using they decide to run a second set of tests. However, the lowest 25% and the highest 35% are not going to be included in the next round of tests. Based on this, what are the upper and lower limits for the energy usage of the light bulbs that will be included in the second round of testing? [269.76 300.24] [278.90, 288.55] [280.22 289.78] [280.22 300.24] QUESTION 31 1. To be accepted to the veterinarian school at State University, applicants must have an entrance exam score within the 95th percentile. If the average score on the entrance exam is 1000 and the exam has a standard deviation of 200, what is the lowest possible score a student needs in order to be accepted to the program if the scores are normally distributed? 1400 1330 1250 1100 QUESTION 32 1. The starting salary for employees at We-B-Burgers are normally distributed with a standard deviation of $5,000. If the mean salary of these employees is $25,000 per year and sixty-eight of them earn more than $35,600 per year how many people are employed by We-B-Burgers? 4,000 2,500 2,000 4,100 QUESTION 33 1. Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally with a mean of 30 minutes and a standard deviation of 8 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15% of the customers should receive this discount. What are the numbers of minutes they need to wait to receive the discount? 34.48 minutes 21.68 minutes 25.52 minutes 38.31 minutes QUESTION 34 1. Suppose the distribution of personal daily water usage in New York City is normally distributed with a mean of 15 gallons and a variance of 25 gallons. Because of a current problem with the distribution of water to its citizens, the mayor wants to give a city tax rebate to the 15 percent of the population who use the least amount of water. What should he use as the water limit for a person to qualify for a city tax rebate? 15.00 gallons 12.20 gallons 9.83 gallons 10.25 gallons QUESTION 35 1. The average time a worker spends on the Internet looking at their personal social media accounts during business hours is 49 minutes per day. Assume the standard deviation is 16 minutes and that the times are normally distributed. For the 10% who spend the most time looking at their personal social media accounts during business hours, how much time do they spend? 28.52 minutes 69.48 minutes 86.28 minutes 11.72 minutes QUESTION 36 1. In grading eggs into small, medium, and large, the Nancy Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal. The value of the mean is and the value of the standard deviation is QUESTION 17 1. The weekly earnings of bus drivers are normally distributed with a mean of $395. If only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers? QUESTION 38 1. Gilligan Boatworks has received more warranty claims this year associated with cracking in the exterior finish of the hull. Gel coat that is too thin negatively affects the finish over the life of the boat because of exposure to salt water and sunlight, so Gilligan wants to start his failure analysis with gel coat. He gets his production supervisor to collect data about the gel coat process and it is determined that the average thickness of the coating is 15mm with a standard deviation of 2.5mm. In order to ensure that no more than 2.5% of the hulls are "too thin" what is the minimum thickness of the gel coat? 19.9mm 10.1mm 13.8mm 14.9mm QUESTION 39 1. The average life expectancy of the Big Daddy air compressor is 6 years with a standard deviation of 8 months. Assume that the lives of the air compressors are normally distributed. If 155 of this year's air compressor production fail to operate properly in less than 4 years and 4 months, how many air compressors were produced this year? 25,000 314 250 2,536 QUESTION 40 1. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? 90.51 93.2 88.51 100.00 QUESTION 41 1. A national survey conducted in 2017 asked employed adults from age 25 to 70 if they plan to keep a foot in the working world after retirement. Thirty-three percent of the respondents answered "very likely". A random sample of 75 adults from this age group was asked the same question. Using the normal approximation to the binomial distribution, what is the probability that more than 18 adults from this sample would "very likely" plan to keep a foot in the working world after retirement? 0.9370 0.6772 0.8413 0.5557 QUESTION 42 1. According to the National Movie Theater Owners Association, 26.0% of movie goers sneak candy and drinks into the theater to avoid the high prices at the concession stand. A random sample of 90 movie goers was taken and they were asked whether they had ever "snuck" candy or drinks into the theater to avoid the high prices at the concession stand. Using the normal approximation to the binomial distribution, what is the probability that fewer than 19 people from this sample said they had? 0.1190 0.2530 0.4149 0.3879 QUESTION 43 1. Tropical Sun, a new brand of suntan lotions is determining whether their new scent, "Wet Sand" will appeal to beach goers. A national survey determined that 33% of people found the smell appealing, and they were encouraged by these results. They are now conducting their own survey and randomly sample 75 people and ask them if the new scent is appealing. What is the probability that between 20 and 23 people will say that they find the scent appealing. Use the normal approximation to the binomial when solving for the probability. 0.1510 0.4560 0.278 0.6539 QUESTION 44 The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500. a. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor's? b.Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes? c. What are the minimum and the maximum incomes of the middle 95% of the residents? d.Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City

Tutor Answer

uoscar
School: UIUC

The solution is attached.Please, give me feedback.

QUESTION 1
1. The weight of softballs is uniformly distributed over the interval of
8 to 12 ounces, inclusively. What is the probability that a randomly selected softball will weigh
between 13 and 15 ounces?

0.250
0.500
0.375
0.000
1.000

QUESTION 2
1. If the weight of softballs is uniformly distributed over the interval of
8 to 12 ounces, inclusively then what is the probability that a randomly selected softball will
weigh more than 10 ounces?
0.750
0.000
0.333
0.500
0.900

QUESTION 3
1. The time it takes (in minutes) to change a flat tire is uniformly distributed. The time is
distributed over a uniform interval of 20 to 30 minutes, inclusively. What is the probability that
the change of a flat tire will be completed in 21.75 to 24.25 minutes?
0.250
0.333

0.375
0.000
1.000
QUESTION 4
Z is a normally distributed random variable. The distribution of Z has a mean equal to 0 and a standard
deviation equal to 1. What is the probability that z will be less than 1.3 or P(Z -1.1)?
0.36432
0.8643
0.1357
-0.1357
-0.8643
QUESTION 6
The number of miles a Ford Explorer is driven before needing a major repair is known to be normally
distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles. What is the probability
that a randomly selected Explorer will travel at least 50,000 miles before needing a major repair?
0.0228
0.9772
0.5000

0.4772
1.0000
QUESTION 7
1. The net gain on an investment in gold is normally distributed with a mean of $10,000 and a
standard deviation of $5,000. What is the probability that an investor will realize a net gain of at
least $5,000 on his investment in gold?
0.1859
0.3413
0.8413
0.4967
0.5000

QUESTION 8
1. The diameter of flex piping used in commercial heating systems is normally distributed with a
mean of 30.5 inches and a standard deviation of 0.20 inches. What is the probability that a
randomly selected section of flex pipe will have a diameter of less than 31 inches?
0.00
0.9938
.8289
.5987
QUESTION 9
1. An apple juice producer buys all his apples from a conglomerate of apple growers in one
northwest state. The amount of juice squeezed from each of these apples is approximately
normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.
What is the probability that a randomly selected apple will contain between 2.00 and 3.00
ounces of juice?
.0475
.4525

.9525
.9554

QUESTION 10
1. An apple juice producer buys all his apples from a conglomerate of apple growers in one
northwest state. The amount of juice squeezed from each of these apples is approximately
normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.What is
the probability that a randomly selected apple will contain between 2.00 and 2.15 ounces?
.4525
.2039
.2486
.7011
QUESTION 11
1. The organizers of the "Holy Smokes Marathon" provide bottled water to the participants and
spectators during the race. Based on data collected in the past, the organizers know that the
number of bottles of water passed out is normally distributed with a mean of 200 bottles and a
standard deviation of 20 bottles. Based on this information, what is the probability that at this
year's race they will hand out between 180 and 210 bottles of water?
.6915
.1915
.5328
.1587
QUESTION 12
1. The starting salaries of individuals with a B.A. in Art History are normally distributed with a mean
of $40,000 and a standard deviation of $5,000. If an individual with a B.A. in Art History is
randomly selected, what is the probability that his or her starting salary will b...

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Anonymous
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