Question

High school text books don't last forever. The lifespan of all high school statistics textbooks is approximately

normally distributed with a mean of 9 years and a standard deviation of 2.5 years. What percentage of the

books last more than 10 years?

34.5%

84.5%

O O O O O

65.5%

11.5%

69%

Answer 1

34.5%

Explanation:

When the distribution is normal, we use 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 question, we have that:

`\mu = 9, \sigma = 2.5`

What percentage of the books last more than 10 years?

As a proportion, this is 1 subtracted by the pvalue of Z when X = 10. So

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

`Z = (10 - 9)/(2.5)`

`Z = 0.4`

`Z = 0.4` has a pvalue of 0.655

1 - 0.655 = 0.345

So

34.5% of the books last more than 10 years.