Suppose that IQ scores have a bell-shaped distribution with a mean of 99 and a standard deviation of 12. Using the empirical rule, what percentage of IQ scores are less than 87? Please do not round your answer.

Question

87-99 = -12/12 = -1

I get stuck here. I know 1 standard deviation lies between 68%.

Answer 1

87 is 1 SD below mean. 68% are
±1 SD, therefore 34% are below the mean, leaving 50% - 34% = 16%

Here is another way to figure it out exactly.

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score. Multiply by 100 to get percentage.

Answer 2

16%