5 Suppose that on average electricians earn approximately 5

5) Suppose that, on average electricians earn approximately $ 54,000 per year in the U.S. Assume that the distribution for electrician’s yearly earnings is normally distributed and that the standard deviation is $ 12,000. What is the probability that the average salary of four randomly selected electricians is more than $50,000, but less than $60,000? Please remember to include the four randomly selected electricians in your equation.

0.5988

0.7486

0.8413

0.9048

Solution

Mean ( u ) =54000
Standard Deviation ( sd )=12000
Number ( n ) = 4
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 50000) = (50000-54000)/12000/ Sqrt ( 4 )
= -4000/6000
= -0.6667
= P ( Z <-0.6667) From Standard Normal Table
= 0.25249
P(X < 60000) = (60000-54000)/12000/ Sqrt ( 4 )
= 6000/6000 = 1
= P ( Z <1) From Standard Normal Table
= 0.84134
P(50000 < X < 60000) = 0.84134-0.25249 = 0.5889 ( + or - 0.011) = 0.5988