Question

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 260 minutes and a standard deviation of 50 minutes.

What is the probability that a battery lasts more than 4 hours?

Answer 1

65.54% probability that a battery lasts more than 4 hours

Explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 260, \sigma = 50`

What is the probability that a battery lasts more than 4 hours?

4 hours is 4*60 = 240 minutes.

So this is 1 subtracted by the pvalue of Z when X = 240.

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

`Z = (240 - 260)/(50)`

`Z = -0.4`

`Z = -0.4` has a pvalue of 0.3446

1 - 0.3446 = 0.6554

65.54% probability that a battery lasts more than 4 hours