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andrezito [222]
3 years ago
11

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
Mathematics
1 answer:
zvonat [6]3 years ago
3 0

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.

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Answer:

\displaystyle Range: Set-Builder\:Notation → [y|-2 ≤ y] \\ Interval\:Notation → [-2, ∞) \\ \\ Domain: Set-Builder\:Notation → [x|-4 ≤ x] \\ Interval\:Notation → [-4, ∞)

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<em>See above graph</em>

I am joyous to assist you anytime.

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