Question

IQ scores can be described by a Normal model with mean 100 and standard deviation 15. Find an exact answer to the following questions. (Enter your answer to four decimal places.)

How would I go about solving the following?

(a) What proportion of people are predicted to have an IQ greater than 78?

(b) What proportion of people are predicted to have an IQ less than 109?


(c) What proportion of people are predicted to have an IQ greater than 109?


(d) What proportion of people are predicted to have an IQ between 119 and 139?

Answer 1

Let X = IQ scores

therefore X follows Normal model with mean 100 and standard deviation 15.

a) Here we want to find P( X > 78 ) = 1 - P( X < 78 ) ....( 1 )

Let's use excel:

P( X < 78 ) = "=NORMDIST(78,100,15,1)" = 0.0712

Plug this value in equation ( 1 ), we get.

P( X > 78 ) = 1 - 0.0712 = 0.9288

b) Here we want to find P( X < 109 )

P( X < 109 ) = "=NORMDIST(109,100,15,1)" = 0.7257

c) Here we want to find P(X > 109) = 1 - P( X < 109) = 1 - 0.7257 = 0.2743

d) Here we want to find P( 119 < X < 139 ) = P(X < 139 ) - P (X < 119) ....( 2 )

P(X < 139 ) = "=NORMDIST(139,100,15,1)" = 0.9953

P(X < 119 ) = "=NORMDIST(139,100,15,1)" = 0.8974

Plug these values in equation ( 2 ), we get.

P( 119 < X < 139 ) = 0.9953 - 0.8974 = 0.0980