Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between 61 and 139​? ​

(b) What percentage of people has an IQ score less than 74 or greater than 126? ​

(c) What percentage of people has an IQ score greater than 126?

Answer 1

Ans:

Given that

mean=100 and standard deviation=13

Empirical rule:

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

a)61 and 139 are 3 standard deviations below and above the mean respectively.

So,99.7% of the people  has an IQ score between 61 and 139​.

99.7%

b)74 and 126 are 2 standard deviations below and above the mean respectively.

As,95% of the data falls within 2 standard deviations,so rest 5% falls outside these limits.

5%

c)126 is 2 standard deviations above the mean.

As 5% falls below and above 2 standard deviations,so half of 5% i.e. 2.5% will fall above 2 standard deviations.

2.5%