If you have a normally distributed set of data IQ test with

If you have a normally distributed set of data (IQ test) with a mean of 100 and standard deviation of 15, what is the probability that someone scores more than 138 points?

Solution

population mean,u = 100
standard deviation,sigma = 15

probability that someone scores more than 138 points
P(X> 138 ) = P(Z> ((138-100) / 15)
= P(Z> 2.53 )
= 1 - P(Z<2.53)
= 1 - 0.9943
= 0.0057

[To find P(Z<2.53) look in the standard normal table in the row 2.50 and column 0.03(2.53=2.50+0.03), the value obtained is 0.9943]