Question

Some IQ tests are standardized to a Normal model ​N(97,16​). What IQ would be considered to be unusually​ high? Explain.

A. Any IQ score more than 2 standard deviations above the​ mean, or greater than ____​, is unusually high. One would expect to see an IQ score 3 standard deviations above the​ mean, or greater than ____​, only rarely.

B. Any IQ score more than 1 standard deviation above the​ mean, or greater than ____, is unusually high. One would expect to see an IQ score 2 standard deviations above the​ mean, or greater than _____, only rarely.

C. Any IQ score more than 3 standard deviations above the​ mean, or greater than _____​, is unusually high. One would expect to see an IQ score 1 standard deviation above the​ mean, or greater than ____, only rarely.

Answer 1

Solution:

Normal model ​N(97,16​)

= 97 and   = 16 i.e. = 16 = 4

In normal distribution,

a score which is more than 2 standard deviations above the mean i.e. a score which is greater than ( + 2) is considered as unusually high. Also, the chance of any score is 3 standard deviations above the​ mean i.e. a score greater than ( + 3) is rare.

Here, ( + 2) = 97 + (2 * 4) = 105

( + 3) =  97 + (3 * 4) = 109

So , answer is :

A. Any IQ score more than 2 standard deviations above the​ mean, or greater than 105, is unusually high. One would expect to see an IQ score 3 standard deviations above the​ mean, or greater than 109 , only rarely.