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 $133,000. Assume the standard deviation is $41,000. Suppose you take a simple random sample of 49 graduates. Round all answers to four decimal places if necessary.

1. What is the distribution of X? X ~ N(,)
2. What is the distribution of X? X ~ N(,)
3. For a single randomly selected graduate, find the probability that her salary is between $127,914 and $131,243.
4. For a simple random sample of 49 graduates, find the probability that the average salary is between $127,914 and $131,243.
5. For part d), is the assumption of normal necessary? No Yes