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 167000 dollars. Assume the standard deviation is 32000 dollars. Suppose you take a simple random sample of 100 graduates.

Find the probability that a single randomly selected salary is more than 162000 dollars.
P(X > 162000) = _______

Find the probability that a sample of size n=100 is randomly selected with a mean that is more than 162000 dollars.
P(M > 162000) = _________

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 167000

standard deviation = = 32000

P(x > 162000) = 1 - P(x < 162000)

= 1 - P[(x - ) / < (162000 - 167000) / 32000)

= 1 - P(z < -0.1563)

= 1 - 0.4379

= 0.5621

P(x > 162000) = 0.5621

n = 100

M = 167000

M = / n = 32000 / 100 = 3200

P(M > 162000) = 1 - P( < 162000)

= 1 - P[(M - M) / M < (162000 - 167000) / 3200]

= 1 - P(z < -1.5625)

= 1 - 0.0591

= 0.9409

P(M > 162000) = 0.9409