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 $158,000. Assume the standard deviation is $38,000. 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 b. What is the distribution of æ? ¤ ~ N( c. For a single randomly selected graduate, find the probability that her salary is between $145,066 and $154,144. d. For a simple random sample of 14 graduates, find the probability that the average salary is between $145,066 and $154,144.

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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 $158,000. Assume the
standard deviation is $38,000. 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
b. What is the distribution of æ? - N(
c. For a single randomly selected graduate, find
the probability that her salary is between
$145,066 and $154,144.
d. For a simple random sample of 14 graduates,
find the probability that the average salary is
between $145,066 and $154,144.
e. For part d), is the assumption of normal
necessary? O Yes No
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 $158,000. Assume the standard deviation is $38,000. 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 b. What is the distribution of æ? - N( c. For a single randomly selected graduate, find the probability that her salary is between $145,066 and $154,144. d. For a simple random sample of 14 graduates, find the probability that the average salary is between $145,066 and $154,144. e. For part d), is the assumption of normal necessary? O Yes No
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