The Cooper Company discussed in Problem 13-40 has a second contract with a private firm for which it makes fuses for an electronic instrument. The quality control department at Cooper periodically selects a random sample of five fuses and tests each fuse to determine whether it is defective. Based on these findings, the production process is either shut down (if too many defectives are observed) or allowed to run. The quality control department believes that the sampling process follows a binomial distribution, and it has been using the binomial distribution to compute the probabilities associated with the sampling outcomes.
The contract allows for at most 5% defectives. The head of quality control recently compiled a list of the sampling results for the past 300 days in which five randomly selected fuses were tested, with the following frequency distribution for the number of defectives observed. She is concerned that the binomial distribution with a sample size of 5 and a probability of defectives of 0.05 may not be appropriate.
Length (inches) Frequency Under 3.030 5 3.030 and under 3.035 16 3.035 and under 3.040 7 3.040 and under 3.050 20 3.050 and under 3.060 36 3.060 and under 3.065 8 3.065 and over 8 Number of Defectives Frequency 0 209 1 33 2 43 3 10 4 5 5 0

a. Calculate the expected values for the cells in this analysis. Suggest a way in which cells can be combined to assure that the expected value of each cell is at least 5.

b. Using a significance level of 0.10, what should the quality control manager conclude based on these sample data? Discuss.