Question

Toby's Trucking Company determined that on an annual basis, the distance traveled per truck is normally distributed, with a mean of 50,000 miles and a standard deviation of 12,000 miles How many miles will be traveled by at least (equal to and more than) 72% of the trucks?

Answer 1

Answer: 56994 miles

Explanation:

Given : Toby's Trucking Company determined that on an annual basis, the distance traveled per truck is normally distributed with

$\mu=50,000\text{ miles}$

Standard deviation : $\sigma=12,000\text{ miles}$

Let a be the distance traveled by at least 72% of the trucks.

Let X be the random variable that represents the distance traveled by a truck

Then $P(x\geq a)=0.72$

The critical value corresponds to p-value 0.72 :$z=0.5828415$

Also, $z=\dfrac{x-\mu}{\sigma}$

$\Rightarrow\ 0.5828415=\dfrac{a-50000}{12000}\\\\\Rightarrow\ a=12000(0.5828415)+50000=56994.098\approx56994$

Hence, 56994 miles will be traveled by at least (equal to and more than) 72% of the trucks .