Question

Trucks in a delivery fleet travel a mean of 100 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 at least 141 miles in a day. Round your answer to four decimal places.

Answer 1

Solution :

Given, X follows Normal distribution with,

   = 100

   = 38

Find P(X > 141 )

= P[(X - )/ >  ( 141 - )/]

= P[Z > ( 141 - 100 )/38 ]

= P[Z > 1.08 ]

= 1 - P[Z < 1.08 ]

= 1 - 0.8599 ...... ( use z table)

= 0.1401

P(X > 141 ) = 0.1401