Question

A laptop company claims up to 8.1 hours of wireless web usage for its newest laptop battery life. However, reviews on this laptop shows many complaints about low battery life. A survey on battery life reported by customers shows that it follows a normal distribution with mean 7.5 hours and standard deviation 27 minutes. (a) What is the probability that the battery life is at least 8.1 hours

Answer 1

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.

Explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean 7.5 hours

This means that
`\mu = 7.5`

Standard deviation 27 minutes.

An hour has 60 minutes, which means that
`\sigma = (27)/(60) = 0.45`

What is the probability that the battery life is at least 8.1 hours?

This is 1 subtracted by the p-value of Z when X = 8.1. So

`Z = (X - \mu)/(\sigma)`

`Z = (8.1 - 7.5)/(0.45)`

`Z = 1.33`

`Z = 1.33` has a p-value of 0.9082.

1 - 0.9082 = 0.0918

0.0918 = 9.18% probability that the battery life is at least 8.1 hours.