Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 19. Use the empirical rule to determine the following. 43 and 157

Answer 1

Answer: About 99.7%  IQ scores falls within 43 and 157.

Step-by-step explanation:

According to the empirical rule , if a data follows normal distribution then about 99.7% of the population lies with in three standard deviations from mean.

Given:   IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 19.

Since , the graph of normal distribution is bell-shaped , it mean that IQ scores follow normal distribution.

Then, About 99.7%  IQ scores falls within Mean ± 3 (Standard deviation).

i.e. About 99.7%  IQ scores falls within 100± 3(19).

i.e. About 99.7%  IQ scores falls within 100- 57 and 100+57.

i.e. About 99.7%  IQ scores falls within 43 and 157.

Therefore , by empirical rule

About 99.7%  IQ scores falls within 43 and 157.