Question

Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found that the average annual salary for male and female graduates 10 years after graduation was $168,000 and $117,000, respectively. Assume the population standard deviation for the male graduates is $40,000, and for the female graduates it is $25,000.

When calculating values for z, round to two decimal places.

1. What is the probability that a simple random sample of 40 male graduates will provide a sample mean within $10,000 of the population mean, $168,000 (to 4 decimals)?
   
   
2. What is the probability that a simple random sample of 40 female graduates will provide a sample mean within $10,000 of the population mean, $117,000 (to 4 decimals)?
   
   
3. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean?
   - Select your answer -Part (a) because the population mean for males is higherPart (a) because the population standard deviation for males is higherPart (b) because the population mean for females is lowerPart (b) because the population standard deviation for females is lowerItem 3
   
4. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean (to 4 decimals)?

Answer 1

a. We need to find the following probability:

Converting the values into z values:

From the z table this probability is

b. We need to find the following probability:

Converting the values into z values:

From the z table this probability is:

c. We have a higher probability in part b of obtaining a sample estimate within $10000 of the population mean.This is because of the lower population standard deviation for females.

d. We need to find the following probability:

Converting the values into z values:

From the z table, this probability is 0.4960.