The Readylite 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 Readylite with the on-off switch for this flashlight.These switches,on average,fail 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 failing?
A)43 hours
B)45 hours
C)46 hours
D)50 hours
E)54 hours

Question

Quizplus · Accepted Answer

To find the service life that corresponds to a .8944 probability of not failing, we use the Z-score formula in the context of a normal distribution. The Z-score for a .8944 probability (looking up in a standard normal distribution table or using a calculator) is approximately -1.25 (since we are looking at the probability of lasting at least that long, we consider the left side of the distribution). The Z-score formula is Z = (X - μ) / σ, where X is the value we seek, μ is the mean, and σ is the standard deviation. Rearranging the formula to solve for X gives us X = Zσ + μ. Plugging in the values (-1.25 * 4) + 50 = -5 + 50 = 45. Thus, specifying a service life of 45 hours will give a .8944 probability of the switch lasting at least that long.

The Readylite Company Produces a Flashlight Which Is Perfectly Reliable