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Discussion is Due by 12/12.  Everything else is due by 12/15.

w3_assignment.docx
w3_discussion.docx
w3_project.docx
week_3_quiz.docx
week_3_roi_spreadsheet.xlsx

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W3 Written Assignment “Week 3 Assignment” Business Statistics Week 3 Assignment Question 1 Seventy percent of the students applying to a university are accepted. Using the binomial probability tables or Excel, what is the probability that among the next 18 applicants: 1. 2. 3. 4. 5. 6. At least 6 will be accepted? Exactly 10 will be accepted? Exactly 5 will be rejected? Fifteen or more will be accepted? Determine the expected number of acceptances. Compute the standard deviation. Question 2 Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6. 1. What is the probability that a randomly selected exam will have a score of at least 71? 2. What percentage of exams will have scores between 89 and 92? 3. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award? W3 Discussion “The Normal Probability Dist.” Business Statistics The Normal Probability Distribution In §6.2 we are introduced to the Normal Probability Distribution and the special case of the Normal Probability Distribution, the Standard Normal Probability Distribution, which is a Normal Probability Distribution with mean (u) zero and variance (σ2) one. One way to find probabilities from a Standard Normal Distribution is to use probability tables, which are located inside the front cover of your textbook. • • According to the table, what is the probability when z ≤ -1.75? The probability when z ≤ 1.75? What properties of probability distributions and specifically the Normal Probability Distribution do you notice from the two probabilities that you have found in the table? W3 Project Assignment “Project Week 3” Business Statistics Project Week 3 For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadsheet. Using the ROI data set: 1. If we select 7 colleges from a major and then record whether they are of ‘School Type’ ‘Private’ or not, is this experiment a binomial one? Why or why not? 2. For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally distributed. Consider the shape of the histogram and the measures of central tendency (mean and median) to justify your results. Report on each of these with charts and calculations to justify your answers. Question 1 1. A numerical description of the outcome of an experiment is called a descriptive statistic probability function variance random variable Question 2 1. A random variable that can assume only a finite number of values is referred to as a(n) infinite sequence finite sequence discrete random variable discrete probability function Question 3 1. A random variable that may take on any value in an interval or collection of intervals is known as a continuous random variable discrete random variable continuous probability function finite probability function Question 4 1. A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution random variance random variable expected value Question 5 1. The expected value for a binomial probability distribution is E(x) = Pn(1 - n) E(x) = P(1 - P) E(x) = nP E(x) = nP(1 - P) Question 6 1. The variance for the binomial probability distribution is var(x) = P(1 - P) var(x) = nP var(x) = n(1 - P) var(x) = nP(1 - P) Question 7 1. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable? the experiment has a sequence of n identical trials exactly two outcomes are possible on each trial the trials are dependent the probabilities of the outcomes do not change from one trial to another Question 8 1. The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution. x f(x) 0 0.80 1 0.15 2 0.04 3 0.01 The mean and the standard deviation for the number of electrical outages (respectively) are 2.6 and 5.77 0.26 and 0.577 3 and 0.01 0 and 0.8 Question 9 1. The center of a normal curve is always equal to zero is the mean of the distribution cannot be negative is the standard deviation Question 10 1. A normal distribution with a mean of 0 and a standard deviation of 1 is called a probability density function an ordinary normal curve a standard normal distribution none of these alternatives is correct Question 11 1. A negative value of Z indicates that the number of standard deviations of an observation is to the right of the mean the number of standard deviations of an observation is to the left of the mean a mistake has been made in computations, since Z cannot be negative the data has a negative mean Question 12 1. 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 13 1. Z is a standard normal random variable. The P (1.41 ≤ Z ≤ 2.85) equals 0.4978 0.4207 0.9185 0.0771 Question 14 1. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that X is between 1.48 and 15.56 is 0.0222 0.4190 0.5222 0.9190 Question 15 1. Larger values of the standard deviation result in a normal curve that is shifted to the right shifted to the left narrower and more peaked wider and flatter School Type Private Private Private Public Private Public Private Private Private Private Private Private Private Private Private Public Public Private Private Private Best College ROI by Majo 2013: Payscale.com Cost $222,700.00 $176,400.00 $212,200.00 $125,100.00 $212,700.00 $92,910.00 $214,900.00 $217,800.00 $225,600.00 $217,300.00 $226,500.00 $215,500.00 $223,500.00 $226,600.00 $189,300.00 $89,700.00 $87,030.00 $218,200.00 $229,900.00 $148,800.00 30 Year ROI $1,786,000.00 $1,758,000.00 $1,714,000.00 $1,535,000.00 $1,529,000.00 $1,501,000.00 $1,485,000.00 $1,483,000.00 $1,444,000.00 $1,442,000.00 $1,441,000.00 $1,438,000.00 $1,428,000.00 $1,414,000.00 $1,397,000.00 $1,382,000.00 $1,376,000.00 $1,343,000.00 $1,339,000.00 $1,321,000.00 Annual ROI 7.70% 8.40% 7.80% 9.10% 7.40% 10.10% 7.30% 7.20% 7.00% 7.10% 7.00% 7.20% 7.00% 7.00% 7.50% 9.90% 10.00% 6.90% 6.70% 8.10% School Type Private Private Private Private Private Public Private Private Public Private Public Private Public Private Public Public Public Public Private Public Cost $221,700.00 $213,000.00 $230,100.00 $222,600.00 $225,800.00 $87,660.00 $224,900.00 $221,600.00 $125,100.00 $215,700.00 $92,530.00 $217,800.00 $89,700.00 $229,600.00 $101,500.00 $115,500.00 $104,500.00 $69,980.00 $219,400.00 $64,930.00 30 Year ROI Annual ROI $2,412,000.00 8.70% $2,064,000.00 8.30% $1,949,000.00 7.90% $1,947,000.00 8.00% $1,938,000.00 8.00% $1,937,000.00 11.20% $1,915,000.00 7.90% $1,878,000.00 7.90% $1,854,000.00 9.80% $1,794,000.00 7.90% $1,761,000.00 10.60% $1,752,000.00 7.70% $1,727,000.00 10.70% $1,716,000.00 7.50% $1,703,000.00 10.20% $1,694,000.00 9.70% $1,690,000.00 10.10% $1,685,000.00 11.50% $1,676,000.00 7.60% $1,668,000.00 11.70%
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