Time to develop price quotes. A manufacturer of industrial
Chapter , Problem 162SE(choose chapter or problem)
Time to develop price quotes. A manufacturer of industrial wheels is losing many profitable orders because of the long time it takes the firm’s marketing, engineering, and accounting departments to develop price quotes for potential customers. To remedy this problem, the firm’s management would like to set guidelines for the length of time each department should spend developing price quotes. To help develop these guidelines, 50 requests for price quotes were randomly selected from the set of price quotes made last year: the processing time (in days) was determined for each price quote for each department. Several observations are displayed in the table below. The price quotes are also classified by whether or not they were “lost” (i.e., whether or not the customer placed an order after receiving the price quote).
Request Number |
Marketing |
Engineering |
Accounting |
Lost? |
1 |
7.0 |
6.2 |
.1 |
No |
2 |
.4 |
5.2 |
.1 |
No |
3 |
2.4 |
4.6 |
.6 |
No |
4 |
6.2 |
13.0 |
.8 |
Yes |
5 |
4.7 |
.9 |
.5 |
No |
: |
: |
: |
: |
: |
46 |
6.4 |
1.3 |
6.2 |
No |
47 |
4.0 |
2.4 |
13.5 |
Yes |
48 |
10.0 |
5.3 |
.1 |
No |
49 |
8.0 |
14.4 |
1.9 |
Yes |
50 |
7.0 |
10.0 |
2.0 |
No |
a. Construct a stem-and-leaf display for the total processing time for each department. Shade the leaves that correspond to “lost” orders in each of the displays, and interpret each of the displays.
b. Using your results from part a, develop “maximum processing time” guidelines for each department that, if followed, will help the firm reduce the number of lost orders.
c. Generate summary statistics for the processing times. Interpret the results.
d. Calculate the z-score corresponding to the maximum processing time guideline you developed in part b for each department, and for the total processing time.
e. Calculate the maximum processing time corresponding to a z-score of 3 for each of the departments. What percentage of the orders exceed these guidelines? How does this agree with Chebyshev’s Rule and the Empirical Rule?
f. Repeat part e using a z-score of 2.
g. Compare the percentage of “lost” quotes with corresponding times that exceed at least one of the guidelines in part e to the same percentage using the guidelines in part f. Which set of guidelines would you recommend be adopted? Why?
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