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 \$190,000. Assume the standard deviation is \$34,000. Suppose you take a simple random sample of 15 graduates. Round all answers to four decimal places if necessary.

1. For a simple random sample of 15 graduates, find the probability that the average salary is between \$180,932 and \$187,421.
2. For part d), is the assumption of normal necessary? NoYes

Business Weekly conducted a survey of recent graduates from the top MBA programs. On the basis of the survey, assume that 80% of the recent graduates annual salary exceeds \$45000. Suppose you take a simple random sample of 66 recent graduates.

Note: round all z scores to 2 decimal places and all other numbers to 4 decimal places.

Find the probability that more than 90% of the 66 recent graduates have an annual salary exceeding \$45000.

Beyond representative sampling, what assumptions are needed to satisfy the requirements for this problem?

• X~binomial and at least 5 successes and failures
• X~normal and n≥30n≥30
• X~normal or n≥30n≥30
• X~binomial and both npnp and nqnq at least 5

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 131000 dollars. Assume the standard deviation is 30000 dollars. Suppose you take a simple random sample of 83 graduates.

Find the probability that a single randomly selected salary is at least 129000 dollars.
P(X > 129000) =

Find the probability that a sample of size n=83n=83 is randomly selected with a mean that is at least 129000 dollars.
P(M > 129000) =

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 \$45,000. Suppose you take a simple random sample of 22 graduates. Round all answers to four decimal places if necessary.

1. For a single randomly selected graduate, find the probability that her salary is between \$136,209 and \$142,906.
2. For a simple random sample of 22 graduates, find the probability that the average salary is between \$136,209 and \$142,906.
3. For part 2), is the assumption of normal necessary? No Yes

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 185000 dollars. Assume the standard deviation is 36000 dollars. Suppose you take a simple random sample of 59 graduates.

Find the probability that a single randomly selected salary is at most 187000 dollars.

Find the probability that a sample of size n=59n=59 is randomly selected with a mean that is at most 187000 dollars.

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 158000 dollars. Assume the standard deviation is 41000 dollars. Suppose you take a simple random sample of 93 graduates.

Find the probability that a single randomly selected salary has a mean value between 157574.8 and 169479.1 dollars.
P(157574.8 < X < 169479.1) =

Find the probability that a random sample of size n=93n=93 has a mean value between 157574.8 and 169479.1 dollars.
P(157574.8 < ¯xx¯ < 169479.1) =

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 144000 dollars. Assume the standard deviation is 45000 dollars. Suppose you take a simple random sample of 70 graduates.

Find the probability that a single randomly selected salary is at most 147000 dollars.

Find the probability that a sample of size n=70n=70 is randomly selected with a mean that is at most 147000 dollars.

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 148000 dollars. Assume the standard deviation is 40000 dollars. Suppose you take a simple random sample of 56 graduates.

Find the probability that a single randomly selected salary is more than 143000 dollars.
P(X > 143000) =

Find the probability that a sample of size n=56n=56 is randomly selected with a mean that is more than 143000 dollars.
P(M > 143000) =

Business Weekly conducted a survey of graduates from several top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is \$180,000. Assume the standard deviation is \$44,000. Suppose you take a simple random sample of 18 graduates.

• What is the standard deviation of distribution of XX?
• What is the standard deviation of ¯¯¯XX¯?
• For a single randomly selected graduate, find the probability that her salary is between \$172,544 and \$185,129.
• For a simple random sample of 18 graduates, find the probability that the average salary is between \$172,544 and \$185,129.
• For part d), is the assumption of normal necessary?

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 \$138,000. Assume the standard deviation is \$44,000. Suppose you take a simple random sample of 19 graduates. Round all answers to four decimal places if necessary.

1. For a single randomly selected graduate, find the probability that her salary is between \$141,759 and \$156,006.
2. For a simple random sample of 19 graduates, find the probability that the average salary is between \$141,759 and \$156,006.

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 123000 dollars. Assume the standard deviation is 30000 dollars. Suppose you take a simple random sample of 88 graduates.

Find the probability that a single randomly selected salary is at least 120000 dollars.
P(X > 120000) =

Find the probability that a sample of size n=88n=88 is randomly selected with a mean that is at least 120000 dollars.
P(M > 120000) =

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, the mean annual salary for graduates 10 years after graduation is 143000 dollars and the standard deviation is 32000 dollars. Suppose you take a simple random sample of 57 graduates. Assume that the population of all salaries for MBA graduates is normally distributed.

Find the probability that a single randomly selected salary that doesn’t exceed 147000 dollars.

Find the probability that a sample of size n=57n=57 is randomly selected with a mean that that doesn’t exceed 147000 dollars.

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 127000 dollars. Assume the standard deviation is 42000 dollars. Suppose you take a simple random sample of 85 graduates.

Find the probability that a single randomly selected policy has a mean value between 124722.2 and 142033.3 dollars.
P(124722.2 < X < 142033.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a random sample of size n=85n=85 has a mean value between 124722.2 and 142033.3 dollars.
P(124722.2 < M < 142033.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

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 \$127,000. Assume the standard deviation is \$41,000. Suppose you take a simple random sample of 45 graduates. Round all answers to four decimal places if necessary.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N( , )
2. For a single randomly selected graduate, find the probability that her salary is between \$123,732 and \$128,688.
3. For a simple random sample of 45 graduates, find the probability that the average salary is between \$123,732 and \$128,688.

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