Question

In Tucson, Arizona, the air pollution index averages 62.5 during the year with a standard deviation of 18. Assuming normality, the index falls within what interval 95% of the time?

Answer 1

Using the empirical rule for a normal distribution. the required interval is within plus and minus two standard deviations from the mean:
62.5 - 36 = 26.5.
62.5 + 36 = 98.5.
The interval is (26.5, 98.5).

Answer 2

The correct answer is:

(26.5, 98.5)

Explanation:

The empirical rule states that in a normal distribution, 68% of data fall within one standard deviation of the mean; 95% of data fall within two standard deviations of the mean; and 99.7% of data fall within three standard deviations of the mean.

Since we want 95% of the data, that means our data will fall within 2 standard deviations.  Since the standard deviation is 18, two standard deviations will be 2*18 = 36.

Two standard deviations below the mean will be 62.5-36 = 26.5.

Two standard deviations above the mean will be 62.5+36 = 98.5.

This makes the interval (26.5, 98.5).