Question

The annual salaries of College Presidents in 1993 had a population mean of $150,000 and standard deviation of $20,000. A random sample of 64 College Presidents is chosen from this population. 11. What is the probability that the sample average salary of this randomly chosen sample is less than $144,300? a. 0.0113 b. 0.0222 c. 0.0375 d. 0.4778 e. 0.6293

Answer 1

We know that:

population mean, mu= $150000

population standard deviation, sigma= $20000

sample size, n= 64

sample mean, xbar= $144300

We know, from the Central Limit Theorem, that the sampling distribution of this sample will have a mean= $150000 and a standard deviation = 20000/sqrt(64)= 20000/8= 5000/2= 2500

Thus,

P(average salary<144300)= P(Z<(144300-150000)/2500)

= P(Z<-2.28) [Note: This value can be found from a z distribution table]

= 0.01130

Thus, the correct answer is option a.