Trucks in a delivery fleet travel a mean of 110 miles per day with a standard deviation of 38 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 132 and 159 miles in a day.

Answer: 0.1824Step-by-step explanation:Given : The mileage per day is distributed normally with Mean : [tex]\mu=110\text{ miles per day}[/tex]Standard deviation :  [tex]\sigma=38\text{ miles per day}[/tex]Let X be the random variable that represents the distance traveled by truck in one day .Now, calculate the z-score :-[tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x= 132 miles per day.[tex]z=\dfrac{132-110}{38}\approx0.58[/tex]For x= 159 miles per day.[tex]z=\dfrac{159-110}{38}\approx1.29[/tex]Now by using standard normal distribution table, the  probability that a truck drives between 132 and 159 miles in a day will be :-[tex]P(132<x<159)=P(0.58<z<1.29)\\\\=P(z<1.29)-P(0.58)\\\\= 0.9014747-0.7190426=0.1824321\approx0.1824[/tex]Hence, the probability that a truck drives between 132 and 159 miles in a day =0.1824