Mathematics: Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 22 miles per day. the mileage per day is distributed normally. find the probability that a truck drives between 100 and 157 miles in a day. round your answer to four decimal places.

I think the answer should be D...

Trucks in a delivery fleet travel a mean of 120 miles

Dweath50

11.03.2022

0.7721

Step-by-step explanation:

Given : Mean : $\mu = 120\text{ miles}$

Standard deviation : $\sigma = 22\text{ miles}$

The formula to calculate the z-score :-

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

For x= 100 miles

$z=\dfrac{100-120}{22}=-0.909090\approx-0.91$

For x= 157 miles

$z=\dfrac{157-120}{22}=1.68181\approx1.68$

The P-value : P(-0.91

$=0.9535213-0.1814113=0.77211\approx0.7721$

Hence, the probability that a truck drives between 100 and 157 miles in a day. = 0.7721

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