Question

Salaries at an organization are normally distributed with a mean of µ = $50,000 with a standard deviation of σ = $15,000. What is the probability of selecting a sample of 40 people with a mean salary of less than $40,000? Which statistic should you use to answer this question?

Answer 1

z statistic will be used because population std dev is given.

µ =    50000                                      
σ =    15000                                      
n=   40                                      
                                          
X =   40000                                      
                                          
Z =   (X - µ )/(σ/√n) = (   40000   -   50000.00   ) / (   15000.000   / √   40   ) =   -4.22  
                                          
P(X < 40000   ) = P(Z < -4.216   ) =   0.000012 (answer)
excel formula for probability from z score is =NORMSDIST(Z)