A population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and x¯ is used to estimate μ . What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)? What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)? 

BusinessWeek conducted a survey of graduates from 30 top MBA programs (BusinessWeek, September 22, 2003). On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000, and for the female graduates it is $25,000. 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)? 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)? 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)?