Aset of data is normally distributed with a mean of 86 and a standard deviation of 1.5. what percent of the data is in the interval 86–87.5?

The correct answer is:

34%.

Explanation:

Using the empirical rule, we know that 68% of the data fall within 1 standard deviation of the mean.

The mean is 86 and the standard deviation is 1.5; this makes 1 standard deviation below the mean 86-1.5=84.5 and 1 standard deviation above the mean 86+1.5=87.5.

This means 68% of the data fall from 84.5 to 87.5.

However, we are only concerned with the interval 86-87.5; this is the interval 1 standard deviation above the mean.

Half of our 68% will fall within this range:

68/2 = 34%.