Find the probability and interpret the results.

Question

Find the probability and interpret the results.
The population mean annual salary for environmental compliance specialists is about $60,000. A random sample of 40 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $58,000? Assume σ=$5,700.

Answer 1

 

  (sample mean - population mean)

--------------------------------------------  =

      standard deviation / sqrt(n)

 

 (58000 - 60000)

--------------------- =

      5700/sqrt(40)

 

 (-2000)

 --------------- =

5700/sqrt(40)

 

-2000

--------

 5700/ 6.3246

 

 -2.219

 

 

Prob ( Z < -2.219) = 0.0132 = 1.32%