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?

(a) 68%

(b) 0.3%

(c) 2.5%

Step-by-step 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