Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 18.

Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 64 and 136​?

​(b) What percentage of people has an IQ score less than
64 or greater than 136​?

​(c) What percentage of people has an IQ score greater than 136?

Answer 1

Q) Given that, mean = 100 and standard deviation = 18

According to Empirical Rule:

i) About 68% of the data fall within 1 standard deviations of the mean.

ii) About 95% of the data fall within 2 standard deviations of the mean.

iii) About 99.7% of the data fall within 3 standard deviations of the mean.

a)

Therefore, from empirical rule ii) about 95% of people has an IQ score between 64 and 136.

b) Since 95% of people has an IQ score between 64 and 136, that only 5% (100% – 95% = 5%) of the people has an IQ score above 136 and below 64

Therefore, 5% of people has an IQ score less than 64 or greater than 136

c) Since exactly 5% of people has an IQ score less than 64 or greater than 136, we need to split that amount in half to determine how much is only above 136.

That is, 5% / 2 = 2.5%

Therefore, 2.5% of people has an IQ score greater than 136.