You may need to use the appropriate appendix table or technology to answer this question. The Economic Policy Institute periodically issues reports on workers' wages. Suppose 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. (Round your answers to four decimal places.) (a) What is the probability that a sample of 90 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 90 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? Why? (d) Calculate the amount that is $0.60 less than the population mean of $27.83. What is the probability that a sample of 140 female graduates will provide a sample mean less than this amount? Step 1 (a) What is the probability that a sample of 90 male graduates will provide a sample mean within $1.00 of the population mean, $37.39? The population mean hourly wage for male graduates was given to be $37.39 with a standard deviation of $4.60. A sample from the population will not necessarily give these same values. Let x represent the sample mean hourly wage for a group of 90 males. To be within $1.00 of the population mean of $37.39 gives a range of hourly wages between X $37.39 $1.00 = $ SX and $37.39+ $1.00 = $ . Therefore, the desired probability that a sample mean of 90 males is within $1.00 of the population mean is