Question

The Speedmaster IV automobile gets an average of 22.0 miles per gallon in the city. The standard deviation is 3 miles per gallon. Find the probability that on any given day, the automobile will get less than 26 miles per gallon when driven in the city. Assume that the miles per gallon that this automobile gets is normally distributed.

Answer 1

91% of the time the auto will get less than 26 mpg

Explanation:

Think of (or draw) the standard normal curve. Mark the mean (22.0). Then one standard deviation above the mean would be 22.0 + 3.0, or 25.0. Two would be 22.0 + 2(3.0), or 28.0. Finallyl, draw a vertical line at 26.0.

Our task is to determine the area under the curve to the left of 26.0.

Using a basic calculator with built-in statistical functions, we find this area as follows:

normcdf(-100, 26.0, 22.0, 3.0) = 0.9088, which is the desired probability: 91% of the time the auto will get less than 26 mpg.