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 $126,000. Assume the standard deviation is $44,000. Suppose you take a simple random sample of 13 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of a? a - N( c. For a single randomly selected graduate, find the probability that her salary is between $110,995 and $123,597.
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 $126,000. Assume the standard deviation is $44,000. Suppose you take a simple random sample of 13 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of a? a - N( c. For a single randomly selected graduate, find the probability that her salary is between $110,995 and $123,597.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Transcribed Image Text:**Business Weekly Salary Survey Analysis**
Business Weekly conducted a survey of graduates from 30 top MBA programs. Based on the survey, assume the mean annual salary for graduates 10 years after graduation is $126,000, with a standard deviation of $44,000. Suppose you take a simple random sample of 13 graduates. Round all answers to four decimal places if necessary.
**Questions:**
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 $110,995 and $123,597.
\(\_\_\_\_\_\_\_\_\_\_ \)
d. For a simple random sample of 13 graduates, find the probability that the average salary is between $110,995 and $123,597.
\(\_\_\_\_\_\_\_\_\_\_ \)
e. For part d), is the assumption of normality necessary?
⬜ No ⬜ Yes
This exercise aims to analyze understanding of normal distribution and probability calculations based on salary data.
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