10 The population mean annual salary for environmental compl

10. The population mean annual salary for environmental compliance specialists is about $61,500. A random sample of 34 specialists is drawn from this population. What is the probability that the mean salary is less than $59,000? Assume standard deviation sigma= $5800?

Solution

Sample size (n) = 34
Mean ( u ) =61500
Standard Deviation ( sd )=5800/ Sqrt ( 34 ) = 994.6918

Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 59000) = (59000-61500)/5800/ Sqrt ( 34 )
= -2500/994.6918= -2.5133
= P ( Z <-2.5133) From Standard NOrmal Table
= 0.006                                      
the probability that the mean salary is less than $59,000 is 0.006