A P/OM student has purchased a four-function calculator for use during exams.This calculator is perfectly reliable except for two parts: its microchip,which has a failure rate of one in every twenty hours of operation; and its battery,which has a failure rate of one in every ten hours of operation.Also,on average the battery will fail in five hours,with a standard deviation of 30 minutes.What service life should the manufacturer specify in order to have a .8413 probability that a battery will not fail within that amount of time?
A)3.5 hours
B)4 hours
C)4.5 hours
D)5 hours
E)5.5 hours

Question

Quizplus · Accepted Answer

The z-score corresponding to a probability of 0.8413 is approximately 1. Using the formula for z-score: z = (X - μ) / σ, where X is the service life, μ is the mean (5 hours), and σ is the standard deviation (0.5 hours), we solve for X: 1 = (X - 5) / 0.5, which gives X = 4.5 hours.

A P/OM Student Has Purchased a Four-Function Calculator for Use