Question

Toby's Trucking Company determined that on an annual basis the distance traveled per truck is normally distributed with a mean of 50.0 thousand miles and a standard deviation of 12.0 thousand miles.

a. What proportion of trucks can be expected to travel between 34.0 and 50.0 thousand miles in the year?

Answer 1

0.4082

Explanation:

Data

mean (
`\mu`) = 50,000 miles

standard deviation (
`\sigma`) = 12,000 miles

expected distance (X) = 34,000 miles

In the figure attached, standard normal distribution table can be seen. Z is computed as follows:

`Z = (X - \mu)/(\sigma){`

`Z = (34000 - 50000)/(12000){`

`Z = -1.33{`

In standard table, the area between 0 and -1.33 is the sem as between 0 and 1.33. So, the proportion of trucks is 0.4082