The following data represent the observed number of defective disks produced each hour based on observing the system for 30 successive hours.

0 3 5 2 6 8 3 5 4 6 6 9 5 1 2 1 2 5 3 3 0 1 0 7 1 7 5 4 4 3

a. Plot a frequency histogram for the numbers of failures per hour.

b. Compute the mean and the variance of the sample. Use the formulas

(Note: You can streamline the calculations by grouping the data first, as there are only 10 distinct values.)

c. If the number of defective disks produced hourly is normally distributed with mean and variance computed in part (b), determine the probability that fewer than five defectives are observed in any particular hour.

d. If each disk costs the company $5 to produce and defective disks are discarded, how long (in an expected-value sense) would it take to pay off a new piece of equipment costing $45,000 that would reduce defectives to half of the current level? Assume 40-hour production weeks and 48 weeks per year.

Transcribed Image Text:

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