Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following. ​

(a) What percentage of people has an IQ score between 40 and 160​? ​

(b) What percentage of people has an IQ score less than 60 or greater than 140​? ​

(c) What percentage of people has an IQ score greater than 140​?

Answer 1

Given that, mean = 100 and standard deviation = 20

According to Empirical rule,

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

(mean - sd = 100 - 20 = 80 and mean + sd = 100 + 20 = 120)

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

(mean - 2sd = 100 - (2*20) = 60 and mean + 2sd = 100 + (2*20) = 140)

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

(mean - 3sd = 100 - (3*20) = 40 and mean + 3sd = 100 + (3*20) = 160)

Therefore,

a) 99.7% of people has an IQ score between 40 and 160​.

Answer : 99.7%

b) 95% of the people has an IQ score between 60 and 140.

Therefore, 100 - 95 = 5% of people has an IQ score less than 60 or greater than 140

Answer : 5%

c) 5/2 = 2.5% of people has an IQ score greater than 140

Answer : 2.5%