# Decision tree, quality control, forecasting

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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.?

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?

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.

4. Using the data in the table below, solve:

(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.

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.

10 .326 .324 .325 .323 .321

b)Five samples are drawn three days after your charts were finished. The data are as follows:

Plot the corrected X-bar and R values on your chart. Comment on the data in the five samples.

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