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In: Statistics and Probability

7.1 The Central Limit Theorem for Sample Means (Averages) Use the following information to answer the...

7.1 The Central Limit Theorem for Sample Means (Averages)

Use the following information to answer the next six exercises: Yoonie is a personnel manager in a large corporation. Each

month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately

four hours each to do with a population standard deviation of 1.2 hours. Let Χ be the random variable representing the time

it takes her to complete one review. Assume Χ is normally distributed. Let X¯ be the random variable representing the meantime to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.

1. What is the mean, standard deviation, and sample size?

426 Chapter 7 | The Central Limit Theorem

This OpenStax book is available for free at http://cnx.org/content/col11562/1.182. Complete the distributions.

a. X ~ _____(_____,_____)

b. X¯ ~ _____(_____,_____)

3. Find the probability that one review will take Yoonie from 3.5 to 4.25 hours. Sketch the graph, labeling, and scaling the

horizontal axis. Shade the region corresponding to the probability.

a.

Figure 7.16

b. P(________ < x < ________) = _______

4. Find the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs. Sketch the graph, labeling

and scaling the horizontal axis. Shade the region corresponding to the probability.

a.

Figure 7.17

b. P(________________) = _______

5. What causes the probabilities in Exercise 7.3 and Exercise 7.4 to be different?

Chapter 7 | The Central Limit Theorem 4276. Find the 95th percentile for the meantime to complete one month's reviews. Sketch the graph.

a.

Figure 7.18

b. The 95th Percentile =____________

Solutions

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