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 $174,000. Assume the standard deviation is $42,000. Suppose you take a simple random sample of 14 graduates. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( 174000 42000 b. What is the distribution of ? @ ~ N( 174000 c. For a single randomly selected graduate, find the probability that her salary is between $165,863 and $178,875. d. For a simple random sample of 14 graduates, find the probability that the average salary is between $165,863 and $178,875. e. For part d), is the assumption of normal necessary? O Yes No