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 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 -1.1)?
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
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