Question

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 18.5 inches, and standard deviation of 3.9 inches. If 36 items are chosen at random, what is the probability that their mean length is greater than 16.8 inches? (Round answer to four decimal places)

Answer 1

Solution:

Given that,

= 18.5

= 3.9

n = 36

So,

= 18.5

=  ( /n) = ( 3.9 / 36 ) = 0.65

p (   > 16.8 )

= 1 - p (   < 16.8 )

= 1 - p ( -  /   ) < ( 16.8 - 18.5 / 0.65)

= 1 - p ( z < - 1.7 /0.65 )

= 1 - p ( z < - 2.62)

Using z table

= 1 - 0.0044

= 0.9956

Probability = 0.9956