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

Question

Mathematics

Mireya Mcintosh

16 November, 18:05

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

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Niko Beard · 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.