Question

Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $61,000. A random sample of 43 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $ 59,000? Assume σ= $6,100.

The probability that the mean salary of the sample is less than $59,000 is ____  (Round to four decimal places as needed.)

Interpret the results. Choose the correct answer below.

A . About 15.8 % of samples of 43 specialists will have a mean salary less than $59,000. This is not an unusual event.

B. Only 15.8 % of samples of 43 specialists will have a mean salary less than $59,000. This is an unusual event.

C.Only 1.58 % of samples of 43 specialists will have a mean salary less than $59,000. This is an unusual event.

D.About 1.58 % of samples of 43 specialists will have a mean salary less than $59,000. This is not an unusual event.

Answer 1

µ =    61000              
σ =    6100              
n=   43              
left tailed                  
X ≤    59000              
                  
Z =   (X - µ )/(σ/√n) =   -2.150          
                  
P(X ≤   59000   ) = P(Z ≤   -2.150   ) =   0.0158 or 1.58%

excel formula for probability from z score is =NORMSDIST(Z)

The probability that the mean salary of the sample is less than $59,000 is 0.0158

                   About 1.58 % of samples of 43 specialists will have a mean salary less than $59,000. This is not an unusual event

[because probability is greater than 5%]