Covercraft manufactures covers to protect automobile interiors and finishes. Its Block-It 200 Series fabric has a limited two-year warranty. Periodic testing is done to determine if the warranty policy should be changed. One such study examined those covers that became unserviceable while still under warranty. Data that could be produced by such a study are contained in the file titled Covers. The data represent the number of months a cover was used until it became unserviceable. Covercraft might want to examine more carefully the covers that became unserviceable while still under warranty. Specifically, it wants to examine those that became unserviceable before they had been in use one year.
a. Determine the number of covers that became unserviceable before they had been in use less than a year and a half.
b. If Covercraft quality-control staff selects 20 of the covers at random, determine the probability that none of them will have failed before they had been in service a year and a half.
c. If Covercraft quality control staff needs to examine at least 5 of the failed covers, determine the probability that they will obtain this many.