Question

I’m struggling with this question. I don’t even know where to start

Answer 1

The empirical rule

The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

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Given,

`\begin{gathered} \mu=100 \\ \sigma=10 \end{gathered}`(a)

% of people who have IQ between 70 and 130...

70 and 130 are 3 standard deviations of the mean.

`\begin{gathered} 70=\mu-3\sigma \\ 70=100-3(10) \\ 70=70 \\ \text{and,} \\ 130=\mu+3\sigma \\ 130=100+3(10) \\ 130=130 \end{gathered}`

So, that is 99.7% of the people.

Answer - 99.7%

(b)

% of people with IQ less than 90 or greater than 110

"90" and "110" are 1 standard deviation of the mean. So, according to the Empirical Rule, 68% of data fall between 1 standard deviation of the mean.

We want to know what % of data falls outside this 1 standard deviation. That will be:

100 - 68 = 32%

Answer - 32%

(c)

% of people with IQ greate than 120

From the diagram above, we see that the region that is greater than 120 is 2.35%

Answer - 2.35%