Question

Correct Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 17 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 130 and 137 miles in a day. Round your answer to four decimal places.

Answer 1

Let , $X\to N(\mu=120,\sigma=17)$

Now , we want to find the $P(130<X<137)$

$P(130<X<137)=P(\frac{130-120}{17}<\frac{X-\mu}{\sigma}<\frac{137-120}{17})$

$=P(0.59<Z<1.00)$

$=P(Z>0.59)-P(Z>1.00)$

$=0.27760-0.15866$ ; Probabilities from normal probability integral table

$=0.1189$

Therefore , the probability that a truck drives between 130 and 137 miles in a day is 0.1189.