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.Assuming that a new battery has just been installed,what is the probability that the battery will perform reliably during a one-hour exam?
A)0.05
B)0.10
C)0.20
D)0.90
E)0.95

Question

Quizplus · Accepted Answer

To find the probability that the battery will perform reliably during a one-hour exam, we need to find the probability that it will not fail during that time period.

The battery has a failure rate of one in every ten hours, so the probability that it will not fail during a one-hour period is:
P(not failing in one hour) = 1 - P(failing in one hour)

To find P(failing in one hour), we can use the fact that the average time until failure is five hours and the standard deviation is 30 minutes. This means that the battery follows a normal distribution with a mean of 5 hours and a standard deviation of 0.5 hours.

We can standardize the one-hour period by subtracting the mean and dividing by the standard deviation:
z = (1 - 5) / 0.5 = -8

Using a standard normal table or calculator, we can find the probability of a standard normal random variable being less than -8 to be virtually 0. Therefore, the probability of the battery failing during the one-hour exam is virtually 0, and the probability of the battery performing reliably during the exam is approximately 1, or 0.90 to be more precise.

Therefore, the best choice is D) 0.90.

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