Question

A manufacturer knows that their items have a lengths that are skewed right, with a mean of 15.8 inches, and standard deviation of 4.7 inches.

If 35 items are chosen at random, what is the probability that their mean length is greater than 13.9 inches?

Answer 1

Since sample size is large enough ( > 30), we can approximate the sampling distribution of sample mean by normal distribution.

µ =    15.8                                      
σ =    4.7                                      
n=   35                                      
                                          
X =   13.9                                      
                                          
Z =   (X - µ )/(σ/√n) = (   13.9   -   15.8   ) / (    4.7   / √   35   ) =   -2.392  
                                          
P(X ≥   13.9   ) = P(Z ≥   -2.39   ) =   P ( Z <   2.392   ) =    0.9916           (answer)
excel formula for probability from z score is =NORMSDIST(Z)