The intelligence quotient IQ test scores for adults are norm

The intelligence quotient (IQ) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 16. What is the probability could select a sample of 64 adults and find that the mean of this sample exceeds 101?

Solution

Mean ( u ) =100
Standard Deviation ( sd )=16
Number ( n ) = 64
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 101) = (101-100)/16/ Sqrt ( 64 )
= 1/2= 0.5
= P ( Z >0.5) From Standard Normal Table
= 0.3085