Question

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 $121,000. Assume the standard deviation is $42,000. Suppose you take a simple random sample of 42 graduates. Round all answers to four decimal places if necessary. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) For a single randomly selected graduate, find the probability that her salary is between $122,679 and $130,519. For a simple random sample of 42 graduates, find the probability that the average salary is between $122,679 and $130,519. For part d), is the assumption of normal necessary? YesNo

Answer 1

X ~ N(121,000, 42,000)

¯ x ~ N(121,000, 6480.7407)

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For part d), is the assumption of normal necessary?

Ans : Yes (because n=42>30, we can use central limit theorem)