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.
Accepted Solution
A:
Answer: 0.7721Step-by-step explanation:Given : Mean : [tex]\mu = 120\text{ miles}[/tex]Standard deviation : [tex]\sigma = 22\text{ miles}[/tex]The formula to calculate the z-score :-[tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x= 100 miles[tex]z=\dfrac{100-120}{22}=-0.909090\approx-0.91[/tex]For x= 157 miles[tex]z=\dfrac{157-120}{22}=1.68181\approx1.68[/tex]The P-value : [tex]P(-0.91<z<1.68)=P(z<1.68)-P(z<-0.91)[/tex][tex]=0.9535213-0.1814113=0.77211\approx0.7721[/tex]Hence, the probability that a truck drives between 100 and 157 miles in a day. = 0.7721