* Source:

Size: px

Start display at page:

Download "* Source:"

Corey Harmon
5 years ago
Views:

Problem: A recent report from Gallup stated that most teachers don t want to be armed in school. Gallup asked K-12 teachers if they would be willing to be trained so they could carry a gun at school.

1 Problem: A recent report from Gallup stated that most teachers don t want to be armed in school. Gallup asked K-12 teachers if they would be willing to be trained so they could carry a gun at school. Eighteen percent of teachers responded that they were willing to be trained to carry a gun at school. Assume that a random sample of nine American K-12 teachers is obtained. Let the random variable x equal the number of teachers out of the sample of nine that are that are willing to be trained to carry a gun in school. Generate the binomial probability distribution for x. * Source: Part I Theoretical Distribution Use STATDISK to generate the binomial probability distribution (see example on p. 20 of the Chapter 6 handouts). Snip or screen print your output distribution for printing. Make sure you get the whole output box, including the input information. Page 1 of 6

2 Part II Experimental Distribution Page 2 of 6

3 Answer Sheet Assignment 6 Part I Theoretical Distribution Fill in all of the blanks: n = 9 s = success = (describe in words) = teacher willing to carry a gun p = 0.18 x = 0 through 9 (possible number of WILLING to carry selected out of 9) 1. Explain why this is a binomial experiment, making sure to address each of the four criteria (given on p. 12 of the Chapter 6 Handouts). 1. There was a fixed number of trials, Each trial was independent. 3. There were two outcomes: Willing to carry a gun, or not. 4. Probability of success was the same for each trial, p = What is the theoretical probability that exactly 2 of the 9 selected From STATDISK, P(2) = What is the theoretical probability that less than 2 of the 9 selected From STATDISK, P(1 or fewer) = What is the theoretical probability that at least 3 of the 9 selected From STATDISK, P(3 or greater) = Page 3 of 6

4 5. Would it be unusual if 4 or more of the 9 selected teachers are WILLING to be trained to carry a gun in school? Explain why or why not, using your results from the theoretical probability distribution. Use the probabilities method on p. 24 of the Chapter 6 Handouts, and you must quote a specific probability here. From STATDISK, P(4 or more) = No, that would NOT be unusual, because the probability is > Make a probability histogram for the theoretical probabilities on the following grid. 7. Describe the shape of the probability distribution, and explain briefly why it has that shape. Specifically, look at p. 22 of the Chapter 6 Handouts, and address the values of both n and p. Calculate the value of np(1 p). It is right-skewed because p < 0.5, and the trial size (n = 9) is small-ish. Specifically, np(1 p) = (9)(0.18)(0.82) = 1.33 which is less than 10. Page 4 of 6

5 8. Show me your hand calculations (using the binomial distribution formulas) for the mean and standard deviation of the theoretical distribution. Mean: : = np = (9)(0.18) = 1.62 Std. Dev.: = np( 1 p) = (9)(0. 18)(0. 82) = Part II Experimental Distribution 1. What was the experimental probability that exactly 2 of the 9 selected From EXCEL, P(2) = What was the experimental probability that less than 2 of the 9 selected From EXCEL, P(less than 2) = P(0) + P(1) = What was the experimental probability that at least 3 of the 9 selected From EXCEL, P(3 or more) = P(3) + P(4) + + P(9) = What was the mean and the standard deviation of the experimental probability distribution? Mean = (1.3) Standard Deviation = (1.2) Page 5 of 6

6 5. Make a probability histogram for the experimental probabilities on the following grid. 6. Comment on/discuss the differences and/or similarities between the experimental and theoretical results for this procedure. Specifically address the differences in the probability distributions (shape), the means and the standard deviations. The probability distributions definitely have the same general shape, leaning to the left, therefore being right-skewed. There are obviously some differences in some of the specific probability values. The means were fairly close (1.3 experimental vs. 1.6 theoretical) and the standard deviations were the same to one decimal place, 1.2 for both. Overall about what you would expect, given that we only ran the experiment a limited number of times (78 runs). If we repeated the experiment many more times, the results would gradually approach the theoretical probabilities. Note that the theoretical distribution does not have a specified number of trials, it is simply what the mathematics predicts should happen in the long run. Page 6 of 6

Chapter 4 Probability Distributions

Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5