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Chapter 6: Problem 89

Stress on the job is a major concern of a large number of people who go into managerial positions. It is estimated that \(80 \%\) of the managers of all companies suffer from job-related stress. a. What is the probability that in a sample of 200 managers of companies, exactly 150 suffer from job-related stress? b. Find the probability that in a sample of 200 managers of companies, at least 170 suffer from job-related stress. c. What is the probability that in a sample of 200 managers of companies, 165 or fewer suffer from job-related stress? d. Find the probability that in a sample of 200 managers of companies, 164 to 172 suffer from job-related stress.

Short Answer

Expert verified
The exact probabilities will depend on the results of the computations in the four steps. Keep in mind that calculating those sums might require a statistical calculator or a computer program.

Step by step solution

01

Calculate the probability of exactly 150 managers suffering from job-related stress.

Following the formula, we find that \( P(X=150) = C(200,150) \cdot 0.8^{150} \cdot (1-0.8)^{200-150} \)
02

Calculate the probability of at least 170 managers suffering from job-related stress.

Here we need to sum the probabilities from 170 to 200: \( P(X\geq 170) = \sum_{k=170}^{200} C(200,k) \cdot 0.8^k \cdot (1-0.8)^{200-k} \)
03

Calculate the probability of 165 or fewer managers suffering from job-related stress.

Here we need to sum the probabilities from 0 to 165: \( P(X\leq 165) = \sum_{k=0}^{165} C(200,k) \cdot 0.8^k \cdot (1-0.8)^{200-k} \)
04

Calculate the probability of 164 to 172 managers suffering from job-related stress.

Here we need to sum the probabilities from 164 to 172: \( P(164 \leq X\leq 172) = \sum_{k=164}^{172} C(200,k) \cdot 0.8^k \cdot (1-0.8)^{200-k} \)

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Most popular questions from this chapter

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