Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 101 and a standard deviation of 12. Using the empirical rule, what percentage of IQ scores are between 77 and 125?

Answer 1

95.44% IQ scores are between 77 and 125

We're given,

Mean (a)=101

standard deviation (b)=12

To find : $P[77 < x < 125]$

Using Empirical Rule:

∴ $P[77 < x < 125]$  $=$ $P[\frac{77-101}{12} < \frac{x-a}{b} < \frac{125-101}{12}]$

$=P[-2 < z < 2]$

$=P[Z < 2]-P[Z < -2]$

$=0.9772-0.0228$

$=0.9544$ =95.44% (approx)

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