Assume that the IQ scores have a normal distribution with mean 100 and standard deviation of 8

Question

Assume that the IQ scores have a normal distribution with mean 100 and standard deviation of 8. Determine the probability that the IQ scores of a randomly selected person is:

a) Less than 106

b) Greater than 108

c) Between96and116

(Draw a clear sketch to illustrate the answer.)

Answer 1

A sketch for the 1st problem looks like this:

Using a TI-84 calculator, hit the "distr" button (2nd, then "vars") and scroll down to "2:normalcdf"

For "lower", you want to put in a number that is very far left. In this case zero will work. If you want to be double sure, use -1E99.

For "upper", type "106"

For "μ" (mean), type "100"

For "σ" (standard deviation), type "8"

Select "Paste" then hit the "enter" button, then hit the "enter" button again

The answer should be 0.7733727206 which is 77.34%

So 77.34% of people have an IQ less than 100.

Repeat for the other problems. For problem 2), select "108" as the lower and 1E99 (or a really big number) for the upper. For problem 3) use 96 for the lower and 116 for the upper