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 87 and 113 ​? ​(b) What percentage of people has an IQ score less than 61 or greater than 139 ​? ​(c) What percentage of people has an IQ score greater than 126 ​?

Answer 1

Ans:

mean=100 and standard deviation=13

a)87 and 113 are one standard deviation below and above the mean respectively.

According to empirical rule,68% of the data falls within one standard deviation of the mean.

so, 68%  of people has an IQ score between 87 and 113.

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

According to empirical rule,99.73% of the data falls within 3 standard deviation of the mean,so 0.27% will fall outside.

so, 0.27% of people has an IQ score less than 61 or greater than 139.

c)126 is 2 standard deviations above the mean.

According to empirical rule,95% of the data falls within 2 standard deviation of the mean,so 5% will fall outside the 2 standard deviations and half of it i.e. 2.5% will be in upper tail.

So, 2.5% of people has an IQ score greater than 126