The mean hourly wage of bottling plant employees in Nelson C

The mean hourly wage of bottling plant employees in Nelson County is $16.50 per hour. What is the likelihood that we could select a sample of 40 bottlers with a mean of $16.75 or more? The standard deviation of the sample is $1.75.

Solution

Mean ( u ) =16.5
Standard Deviation ( sd )=1.75
Number ( n ) = 40
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 16.75) = (16.75-16.5)/1.75/ Sqrt ( 40 )
= 0.25/0.2767= 0.9035
= P ( Z <0.9035) From Standard NOrmal Table
= 0.8169                  
P(X > = 16.75) = 1 - P(X < 16.75)
= 1 - 0.8169 = 0.1831