Production facilities must keep track of injuries on the job by their employees, known as recordables (injuries severe enough that they must be reported to the appropriate government agency). A large chemical plant maintains a sign at the entrance to the plant with the current number of injury-free work days. Assume that on any one day a recordable injury occurs with probability 0.02, and assume that this probability is the same for every day of the week.
(a) What is the probability that the sign at the plant entrance reads 5 days.
(b) What is the probability that the number on the sign is less than 5?
(c) What is the probability that the number on the sign is greater than 5?
(d) What is the average number of days that the plant goes without an injury?
(e) In an attempt to decrease the injury rate at the plant, a safety initiative is undertaken. The next five strings of days without injuries at the plant were 92, 85, 103, 48, and 72. Was the initiative successful in lowering the injury rate? Justify your answer.