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 37 39 1 00 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 x