Question

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.

Answer 1

Answer: 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 : $P(-0.91<z<1.68)=P(z<1.68)-P(z<-0.91)$

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

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