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%

34.5%

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

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:

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

has a pvalue of 0.655

1 - 0.655 = 0.345

So

34.5% of the books last more than 10 years.

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