A population has a mean of 200 and a standard deviation of 50. Suppose a simple random sample of size 100 is selected and T is used to estimate u. Use z-table. a. What is the probability that the sample mean will be within 5 of the population mean (to 4 decimals)? b. What is the probability that the sample mean will be within =10 of the population mean (to 4 decimals)? The Economic Policy Institute periodically issues reports on worker's wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviation for male graduates is $4.60, and for female graduates it is $4.10. Use z-table. Round your answers to four decimal places. a. What is the probability that a sample of 50 male graduates will provide a sample mean within $1.00 of the population mean, $37.39? b. What is the probability that a sample of 50 female graduates will provide a sample mean within $1.00 of the population mean, $27.83? c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $1.00 of the population mean? - Select your answer - v Why? Because the standard error for female graduates is the standard error for male graduates d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.60 below the population mean, $27.83