7.3 Exercise 6

A manufacturing plant has 350 special lamps on its production lines. On any day, each lamp could fail with probability $p = 0 . 0017$. These lamps are critical, and must be replaced as quickly as possible. It takes about one hour to replace a lamp, once it has failed. What is the probability that on any day the loss of production time due to lamp failaures is k or fewer hours, $k = 0 , 1 , 2 , 3 , 4 , 5 ?$