Question 1. The time at which the post person delivers the mail to the Management Department follows a normal distribution. The average delivery time is 2:00 p.m. with a standard deviation of 15 min.
(a) what is the probability that the mail will arrive after 2:30 p.m.?
(b) what is the probability the mail will arrive before 1:36 p.m.?
(c) what is the probability that the mail will arrive between 1:48 p.m. and 2:09 p.m.?
Question 2. A company that manufactures electric thermostats purchases its switches from three different suppliers in the following percentages: 25% from Abel Co., 45% form Best Co., and 30% from Choice Co. On the basis of past records, failures during final testing have been noted for 2.5% of the switches from Abel Co., 1.5% from Best Co., and 1.0% from Choice Co.
(a) What overall fraction of switches can be expected to fail during final testing? (Use a tree diagram to support all of your answers)
(b) If a switches is observed to fail at final testing, what is the probability that it was supplied by Best Co.?
(c) If a thermostat passes final testing, what is the probability that the switch was supplied by Choice Company?
Question 3. John Strange would like to start a small tailor shop, but he has decided that it would not work unless the probability of a successful shop (SS) is .6 or greater, or the probability of an unsuccessful shop (US) is .4 or less. At the present time, he believes that the chances of a successful or unsuccessful tailor shop are about the same. In today’s local paper, there was an article that described a study done on the potential of small shops. He found that the probability of a favorable study given a successful shop (Favorable study/SS) was .9, and the probability of an unfavorable study given successful shop (Unfavorable study/SS) was .1. Furthermore, the probability of an unfavorable study given an unsuccessful shop (Unfavorable study/US) was .7, and the probability of a favorable study given an unsuccessful shop (Favorable study/US) was .3. Using a tree diagram help John make his decision.
Question 4. Using the data in the table below, solve:
|
Year
|
Qtr
|
Sales
|
Year
|
Qtr
|
Sales
|
Year
|
Qtr
|
Sales
|
|
1999
|
1
|
16.2
|
2000
|
1
|
20.8
|
2001
|
1
|
28.7
|
|
|
2
|
18.2
|
|
2
|
24.7
|
|
2
|
41.1
|
|
|
3
|
17.0
|
|
3
|
23.9
|
|
3
|
39.9
|
|
|
4
|
17.0
|
|
4
|
22.0
|
|
4
|
37.2
|
a) Using a 4 period moving average forecast 2002 first quarter sales.
(b) Using exponential smoothing and an alpha of .4, forecast for year 2002, Qtr 1 and find MAD.
(c) Compute the forecast for each of the four quarters of year 2008 using the classical decomposition method.
Question 5. Random samples, each with a sample size of five, are periodically taken from a production line that manufactures batteries. The batteries sampled are tested on a volt meter. The production line has just been modified and a new quality-control plan must be designed. For that purpose, ten random samples
Have been taken over a suitable time period; the test results are given below:
a) Compute and draw the appropriate SQC chart for range and sample mean.
|
Sample No. V1
|
V2
|
V3
|
V4
|
V5
|
|
1
|
0.324
|
0.323
|
0.327
|
0.326
|
0.328
|
|
2
|
0.323
|
0.322
|
0.325
|
0.321
|
0.324
|
|
3
|
0.325
|
0.328
|
0326
|
0.324
|
0.325
|
|
4
|
0.324
|
0.321
|
0.326
|
0328
|
0.327
|
|
5
|
0.325
|
0.329
|
0.330
|
0325
|
0.328
|
|
6
|
0.319
|
0.323
|
0324
|
0331
|
0.326
|
|
7
|
0.326
|
0.330
|
0.329
|
0328
|
0.331
|
|
8
|
0.322
|
0.328
|
0.326
|
0325
|
0.323
|
|
9
|
0.320
|
0323
|
0327
|
0.325
|
0.324
|
|
10 326
|
324
|
325
|
323
|
321
|
b) Five samples are drawn three days after your charts were finished. The data are as follows:
|
Sample No
|
Tested Voltages
|
|
|
to
|
0.321
|
0.323
|
0.327
|
|
2a
|
0.325
|
0.329
|
0.323
|
|
3a
|
0.329
|
0.330
|
0.328
|
|
4a
|
0.325
|
0.320
|
0.324
|
|
5a
|
0.319
|
0.320
|
0.321
|
Plot the corrected X-bar and R values on your chart. Comment on the data in the five samples.