The ACME Freight Co. has containerized a large quantity of 4-megabyte memory chips that are to be
shipped to a personal computer manufacturer in California. The shipment contains 1,000 boxes of mem ory chips, with each box containing a dozen chips. The chip manufacturer calls and says that due to an error in manufacturing, each box contains exactly one defec tive chip. The defect can be detected through an easily administered, nondestructive continuity test using an ohmmeter. The chip maker requests that ACME break open the container, find the defective chip in each box, discard them, and then reassemble the container for shipment. The testing of each chip requires one minute to accomplish.
a. Define a random variable representing the amount of testing time required to find the defective chip in a box of chips. What is the range of the random variable? What is the event space?
b. Define a probability density function for the ran dom variable you have defined in (a). Define a prob ability set function appropriate for assigning prob abilities to events relating to testing time required to find the defective chip in a box of chips.
c. What is the probability that it will take longer than five minutes to find the defective chip in a box of chips?
d. If ACME uses two eight-hour-shif t workers for one shif t each to perform the testing, what is the probability that testing of all of the boxes in the container will be completed?