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

Step-by-step 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=(x-\mu)/(\sigma)`

`\Rightarrow\ 0.5828415=(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 .