Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 96
96
and a standard deviation of 17
17
. Using the empirical rule, what percentage of IQ scores are no more than 79
79
? Please do not round your answer.

Answer 1

a mean =96

and a standard deviation = 17

We need to find percentage of IQ scores are no more than 79

IQ scores are no more than 79 means scores <=79

First we find 79 is how many standard deviation from mean

a mean =96

and a standard deviation = 17

96 - 17 = 79 ( we subtracted standard deviation only once)

So 79 is one standard deviation on the left of mean

the empirical rule for bell shaped graph is attached below

We look at the percentage of area where it is less than 79

So we consider the area on the left of 79

The area is shaded in the graph.

13.5% + 2.5% = 16%

16%  of IQ scores are no more than 79