I need 5B answered showing the math work and and what the distribution would look like

column 5+ d. Dev mean Problem 5 order Expense 22. 328646 47- 4 Use StatCrunch to compute the mean and standard deviation for the 20 sample values that you created for Variable 3 in the survey you constructed in Problem 1 above For this problem only, assume that the sample mean and standard deviation for Variable 3 for the 20 sample values in your survey is the same as the population mean and standard deviation for Variable 3. Suppose that you were to randomly select a new sample of 40 customers from your survey population and observe their responses to Variable 3, Based on this new sample size, compute the following probabilities in Problems 5a and 5b below using your calculator and the appropriate statistical table. Also, for each problem below sketch the appropriate distribution with the probability in question appropriately shown. Note that based on the theory in this course you should be able to answer the problems below, without having to actually create a sample of 40 values for Variable 3. Problem 5a Order Find the probability that the sample mean of Variable 3 (based on the 40 customer selected) is less spendture than 90% of the population mean. [4 marks] Variable 3- Z = ( x -1 ) P ( sample mean is less than How much Didyou, Spend on You order 9090 of the population mean ) X - EX 9090 of = 47.4 0.9= 42.6 6 20 3 2 X = 47.4 = 42. 6647.4 PX 2 42. 66 55 4= 4714' 22 132 86 80 Or= 22.3286 V 40 30 35 2= 20 2=1.34 D = 0.90 85 45 The probability that Z