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 between 120 and 130?

Solution

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

probability that someone scores between 120 and 130
P( 120 <X< 130 )
= P( ((120-100) / 15) <Z< ((130-100) / 15) )
= P( 1.33 <Z< 2.00 )
= P(Z<2) - P(Z<1.33)
= 0.9772 - 0.9082
= 0.069

[To find P(Z<1.33) look in the standard normal table in the row 1.30 and column 0.03 (1.33=1.30+0.03), the value obtained is 0.9082, similarly for P(Z<2.00)]