Question

Trucks in a delivery fleet travel a mean of 80 miles per day with a standard deviation of 30 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 97 and 107 miles in a day. (Round your answer to 4 decimal places)

Answer 1

Answer:  0.1037

Step-by-step explanation:

Given : Mean : $\mu=80\text{ miles per day}$

Standard deviation : $\sigma = 30\text{ miles per day}$

The formula to calculate the z-score is given by :-

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

For x = 97 miles per day ,

$z=\dfrac{97-80}{30}\approx0.57$

For x = 107 miles per day ,

$z=\dfrac{97-80}{30}=0.9$

The P-value =$P(0.57$

$=0.8159398-0.7122603=0.1036795\approx0.1037$

Hence, the probability that a truck drives between 97 and 107 miles in a day = 0.1037