Question

Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 19 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 90 and 139 miles in a day. Round your answer to four decimal place

Answer 1

Given,

= 100 , = 19

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

So,

P( 90 < X < 139) = P(X < 139) - P(X < 90)

= P(Z < ( 139 - 100) / 19) - P(Z < ( 90 - 100) / 19)

= P(Z < 2.05) - P(Z < -0.53)

= 0.9798 - 0.2981 (From Z table)

= 0.6817