Looking at a normal distribution set of data IQ test in whic

Looking at a normal distribution set of data (IQ test) in which the mean is 100 and the standard deviation is 15, what is the probability that someone scores more than 120 points?

Solution

P (X>120)=0.0918

Step 2:

Since ?=100 and ?=15 we have:

P ( X>120 )=P ( X??>120?100 )=P ( X??/? > 120?10/015)

Since Z=x??/ ? and 120?100/ 15=1.33 we have:

P ( X>120 )=P ( Z>1.33 )

Step 3: Use the standard normal table to conclude that:

P (Z>1.33)=0.0918