Question

AMC Inc. evaluates divisional managers in part by the number of consumer complaints senior management receives every month. The expectation is that no more than 20 complaints per division per month should be flagged for corporate attention. A sample of divisional data for the last five years or 60 months was collected. AMC defined X to be a random variable counting the number of complaints when twenty or more complaints in any division required senior management attention in a month; f(X) is the relative frequency of X. 30% of all complaints requiring corporate attention fell into this category and were included in the sample. OPEN THE EXCEL EXAM TWO FILE. THE SPREADSHEET FOR THIS PROBLEM IS FOUND ON SHEET ONE. COMPLETE AND SAVE YOUR WORK IN EXCEL AND ENTER THE SOLUTIONS BELOW. 1. (5 points) What is the probability that X = 21? In one sentence, explain how you know. 2. (5 points) What is the probability that more than 24 complaints are received per month? Type the answer and any work below. 3. (5 points) What is the probability that fewer than 24 complaints are received per month? Type the answer and any work below. 4. (5 points) How many complaints in this sample are expected per month? Type the answer below. Is your answer the expected number of all complaints that required corporate attention each month? Write one sentence, explaining your answer. 5. (5 points) What is the standard deviation of complaints of more than 20 per quarter requiring corporate attention? Type the answer below. Complete the spread sheet. Enter column headings in blue. Final answers are entered in the yellow cells. Intermediate calculations are entered in the green cells. To see the underlying equations, press the Ctrl and ~ keys simulataneously.
X	f(X)	Xbar
20	0.051
21
22	0.136
23	0.217
24	0.275
25	0.154
26	0.061
27	0.033
Xbar =						VAR
						ST DEV

Answer 1

1. 1 - 0.927 = 0.073

2. 0.523

3. 0.477

4. Expected number = 23.463

5. 2.640631

X	f(X)	X*f(X)	X²*f(X)
20	0.051	1.02	20.4
21	0.073	1.533	32.193
22	0.136	2.992	65.824
23	0.217	4.991	114.79
24	0.275	6.6	158.4
25	0.154	3.85	96.25
26	0.061	1.586	41.236
27	0.033	0.891	24.057
Xbar =	1	23.463	553.153