Question

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 17 Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 83 and 117 ? (b) What percentage of people has an IQ score less than 49 or greater than 151? (c) What percentage of people has an IQ score greater than 134?

Answer 1

(a) 68%

(b) 0.3%

(c) 2.5%

Explanation:

Data

• mean = 100

• standard deviation (sd) = 17

(a) mean - sd = 100 - 17 = 83

mean + sd = 100 + 17 = 117

The 68–95–99.7 rule states that 68% of the values are within mean ± 1 sd

(b) mean - 3*sd = 100 - 3*17 = 49

mean + 3*sd = 100 + 3*17 = 151

The 68–95–99.7 rule states that 100% - 99.7% = 0.3% of the values are beyond mean ± 3 sd

(c) mean + 2*sd = 100 + 2*17 = 134

The 68–95–99.7 rule states that 95% of the values are within mean ± 2 sd , this means that 5/2 = 2.5% of the values are below mean - 2 sd, and 2.5% are above mean + 2 sd