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Q.5

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Introductory Statistics
Found in: Page 427
Introductory Statistics

Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

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Short Answer

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 1.2hours. 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.

What causes the probabilities in Exercise 7.3andExercise 7.4to be different?

Here, X and x- are two different variables, and the distribution of X and x- have the same means but different standard deviations. The distribution of X is more spread than x-. This causes the probabilities, P(3.5<x<4.25) and P(3.5<x-<4.25) to be different.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Given Information

The required probability in Exercise 7.3 is P(3.5<x<4.25) and in Exercise 7.4 is P(3.5<x-<4.25).

Step 2: Explanation

We have to evaluate the probability that required to be computed in Exercise 7.3 and in Exercise 7.4.

The required probability in Exercise 7.3 is P(3.5<x<4.25) and in Exercise 7.4 is P(3.5<x-<4.25).

According to the information, It is also given that, X follows a normal distribution with mean =4 and standard deviation =1.2.

The sample size is n=1.6.

Here, X indicates the time taken to complete one review and x- represents the mean time taken to complete the 16 reviews.

Step 3: Explanation

Since, X~N(μx=4,σx=1.2), the distribution of the sample mean is

X¯~N(μX,σXn).Thus,

X¯−N(4,1.216)

X¯−N(4,0.3)

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