Suppose that IQ scores have a bell-shaped distribution with a mean of 97 97 and a standard deviation of 18 18 . Using the empirical rule, what percentage of IQ scores are greater than 79 79 ? .

Question

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

Answer 1

Prob( x > 79) = 1 - prob( x < 79)

= 1 - prob( z < (79-97)/18)

= 1 - prob( z < -18/18)

= 1 - prob( z < -1)

= 1 - 0.158655

= 0.841345

Now , per the Empirical rule, roughly 2/3 of the data lies within 1 standard deviation

of the mean average, which is symmetric about the mean average. (The exact

percentage is in question, but it is usually 67-68%)

So 1/3 of the data lies between -1 and 0 and 1/3 of the data lies between

0 and 1 on the bell curve.

So then approximately 1/3 + 1/2 = 2/6 + 3/6 = 5/6 = 0.83

of the data lies on or above -1

This is consistent with the previous result