IQ scores are normally distributed with a mean of 100 and a

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability a random sample of 40 people have a mean IQ score more than 80?

Solution

Mean ( u ) =100
Standard Deviation ( sd )=15
Number ( n ) = 40
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 80) = (80-100)/15/ Sqrt ( 40 )
= -20/2.372= -8.4327
= P ( Z >-8.4327) From Standard Normal Table
= 1