Question

A trucking company determined that the distance traveled per truck per year is normally​ distributed, with a mean of 80 thousand miles and a standard deviation of 11 thousand miles.

What percentage of trucks can be expected to travel either less than 60 or more than 95 thousand miles in a​ year?

Answer 1

Solution :

Given that,

mean = = 80

standard deviation = = 11

a ) P( x < 60 )

P ( x - / ) < ( 60 - 80 / 11)

P ( z < - 20 / 11 )

P ( z < -1.82 )

= 0.0344

P (x > 95 )

= 1 - P (x < 95 )

= 1 - P ( x -  / ) < ( 95 - 80 / 11 )

= 1 - P ( z < 5 / 11 )

= 1 - P ( z < 0.45 )

Using z table

= 1 - 0.6736

= 0.3264

= 0.0344 + 0.3264

Probability= 0.3608 =36.08%