Business Weekly conducted a survey of graduates from 30 top MBA programs. On the

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 43000 dollars. Suppose you take a simple random sample of 75 graduates. Find the probability that a single randomly selected salary that doesn't exceed 168000 dollars. Answer = Find the probability that a sample of size n = 75 n=75 is randomly selected with a mean that that doesn't exceed 168000 dollars. Answer =

Explanation / Answer

(first part)here we use standard normal variate z=(x-mean)/sd

mean=167000, sd=43000, n=75

answer=0.5093

for x=168000, z=(168000-167000)/43000=0.0233

P(x<168000)=P(z<0.0233)=0.5093

(second part)answer=0.5798

here standand deviation of sample mean will be=sd/sqrt(n)=43000/sqrt(75)=4965.21

for x-=168000, z=(168000-167000)/4965.21=0.2014

P(x-<168000)=P(z.<0.2014)=0.5798

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