MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $178,000. Assume the standard deviation is $44,000. Suppose you take a simple random sample of 45 graduates. **Round all answers to four decimal places if necessary.**
a. What is the distribution of \(X\)? \(X \sim N(\_\_\_\_\_, \_\_\_\_\_)\)
b. What is the distribution of \(\bar{x}\)? \(\bar{x} \sim N(\_\_\_\_\_, \_\_\_\_\_)\)
c. For a single randomly selected graduate, find the probability that her salary is between $169,561 and $175,241.
d. For a simple random sample of 45 graduates, find the probability that the average salary is between $169,561 and $175,241.
e. For part d), is the assumption of normal necessary?
- No
- Yes
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Transcribed Image Text:Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is $178,000. Assume the standard deviation is $44,000. Suppose you take a simple random sample of 45 graduates. **Round all answers to four decimal places if necessary.**
a. What is the distribution of \(X\)? \(X \sim N(\_\_\_\_\_, \_\_\_\_\_)\)
b. What is the distribution of \(\bar{x}\)? \(\bar{x} \sim N(\_\_\_\_\_, \_\_\_\_\_)\)
c. For a single randomly selected graduate, find the probability that her salary is between $169,561 and $175,241.
d. For a simple random sample of 45 graduates, find the probability that the average salary is between $169,561 and $175,241.
e. For part d), is the assumption of normal necessary?
- No
- Yes
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