The Ready Light Company produces a flashlight which is perfectly reliable except for two components: the battery, which has a random failure rate of one in every five hours of operation; and the light bulb, which has a random failure rate of three in every ten hours.
Devices, Inc. supplies Ready Light with the on-off switch for this flashlight. These switches, on average, wear out in fifty hours with a standard deviation of four hours. What service life should Devices specify to have a .8944 probability that a switch will last at least that long before wearing out?
46 hours
50 hours
54 hours
45 hours
43 hours