Question

Motorcycles with a certain type of mileage that're normally distributed with a mean of 23.9 mpg with a standard deviation of 1.2 mpg. If 13 motorcycles of this type are randomly selected, find the probability that their average mileage is between 24 and 26 mpg.

Answer 1

Solution :

Given that ,

mean =   = 23.9

standard deviation = = 1.2  

n = 13

= 23.9

=  / n= 1.2 / 13=0.3328

P(24<     <26 ) = P[(24-23.9) / 0.3328 < ( - ) /   < (26-23.9) /0.3328 )]

= P(0.30 < Z < 6.31)

= P(Z <631 ) - P(Z <0.30 )

Using z table

=1-0.6179

=0.3821

probability= 0.3821