Question

Select the correct answer.

The numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation
conclude?
30 pages, what can you
CA
About 60% of the books have fewer than 150 pages.
B.
About 16% of the books have fewer than 150 pages.
c.
About 95% of the books have more than 150 pages.
D
About 16% of the books have more than 150 pages.

Answer 1

B.

About 16% of the books have fewer than 150 pages.

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 180, standard deviation = 30.

150 pages:

150 is 180 - 30 = 1 standard deviation below the mean.

We have that approximately 68% of measures are within 1 standard deviation of the mean, so 100 - 68 = 32% are more than one standard deviation.

The normal distribution is symmetric, which means that of those 32%, 32/2 = 16% are more than 1 standard deviation below the mean, that is, below 150.

So the correct answer is given by option B.