Business Week conducted a survey of graduates from 30 top MBA programs (Business Week, September 22, 2003). The survey found thatthe average annual salary for male and female graduates 10 yearsafter graduation was $168,000 and $117,000, respectively. Assumethe population standard deviation for the male graduates is $45,000, and for the female graduates it is $22,000.
1. What is the probability that a simple random sample of 40 malegraduates 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. 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)?