Question

Scores of an lQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 89 and 1117 (b) What percentage of peopleasa Q score less than 78 or greater than 122? (C) What percentage of people has an IQ score greater than 111? (a) )%(Type an integer or a decimal.) (D)0% (Type an integer or a decimal ) (C) (Type an integer or a decimal.)

Answer 1

Given that, mean $(\mu)$ = 100 and standard deviation $(\sigma)$ = 11

According to empirical rule,

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

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

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

$\text { i) } \mu -\sigma = 100 - 11 = 89 \text { and } \mu + \sigma = 100+ 11 = 111$

$\text { ii) } \mu -2\sigma = 100 - (2*11) = 78 \text { and } \mu +2 \sigma = 100+ (2*11)= 122$

$\text { iii) } \mu -3\sigma = 100 - (3*11) = 67 \text { and } \mu +3\sigma = 100+ (3*11)= 133$

Therefore,

a) 68% of the people has an IQ score between 89 and 111

b) 2.5% of the people has an IQ score less than 78 or greater than 122

c) 16% of the people has an IQ score greater than 111