Part A- The following data represents the number of customer complaint calls per week (to a customer service center) and the respective sample z-scores for a random sample of 20 weeks.
| # of calls |
100.0000 |
120.0000 |
130.0000 |
140.0000 |
150.0000 |
160.0000 |
180.0000 |
190.0000 |
200.0000 |
210.0000 |
| z-score |
-1.9378 |
-1.5483 |
-1.3535 |
-1.1588 |
-0.9640 |
-0.7693 |
-0.3798 |
-0.1850 |
0.0097 |
0.2045 |
| # of calls |
210.0000 |
220.0000 |
220.0000 |
230.0000 |
240.0000 |
250.0000 |
250.0000 |
260.0000 |
260.0000 |
270.0000 |
| z-score |
0.2045 |
0.3992 |
0.3992 |
0.5940 |
0.7887 |
0.9835 |
0.9835 |
1.1782 |
1.1782 |
1.3730 |
Use this data to complete Questions 1 - 6. (You may use the data files or do the calculations by hand.) Questions 1 - 6:
1. Find the mean number of customer complaint calls per week.
2. Find the median number of customer complaint calls per week.
3. Find the variance for the number of customer complaint calls per week.
4. Find the standard deviation for the number of customer complaints per week.
5. Find the 3-sigma limits for the number of customer complaints calls per week.
6. Based on the sample z-scores (given in the data), are there any extreme outliers?
Part B- A dog food manufacturing plant experiences an average of 2 production line shutdowns per week. Suppose that shutdowns occur at random according to a Poisson distribution with parameter p = 2 (represents the average number of line shutdowns per week).
Use this above given information to complete Questions 7 - 9:
7. Which distribution should be used for this problem? (Binomial, Poisson or Normal)
8. What is the probability that, in a given week, there will be exactly 3 line shutdowns?
9. What is the probability that, in a given week, there will be at least two line shutdowns?
Part C- A production process that creates 128 Gb flash drives operates with 5% defective rate. Every 15 minutes, a sample of 25 flash drives is selected at random and the number of defective flash drives counted. A sample has just been selected. Use this information to complete Questions 10 - 13.
10. Which distribution should be used for this problem? (Binomial, Poisson or Normal)
11. What is the probability that there are 2 defective flash drives?
12. If one or more defective flash drives are found, the production process is stopped so that the problem can he investigated. Find the probability that the process will be stopped.
13. How many defective flash drives would you expect to see if the 5% defective rate is correct?
Part D- Suppose Matt & Rodrigo know the specification limits for a dog food bag filling machine are 30.0 ± 1.25 pounds. In other words, the filling process is considered to be functioning at an appropriate level (functioning 'in control") if the amount of fill in the dog food bags is between 28.75 pounds and 31.25 pounds. Suppose the filling process is normally distributed with a mean of 30 pounds and a standard deviation of 0.50 pounds. Matt & Rodrigo select a bag of dog food at random from the assembly line. Let X - amount of fill (amount of dog food) in the bag
Use this information to complete Questions 14 - 19.
14. Which distribution should be used for this problem? (Binomial, Poisson or Normal)
15. Find the probability that the bag is under-filled; i.e., the fill is less than 28.75 pounds.
16. Find the probability that the bag is not under-filled; i.e., the fill is at least 28.75 pounds.
17. Find the probability that the bag has a fill amount that meets specifications, i.e., has a fill amount that is between, and, including, 28.75 and 31.25 pounds.
18. If 5,000 bags are filled, approximately how many would fail to meet a minimum fill amount of 28.75 pounds?
19. Find the 95th percentile (i.e., find x such that P(X < x) = 0.95).