Suppose that IQ scores have a bell-shaped distribution with a mean of 101 and a standard deviation of 12. Using the empirical ru

Question

1 year ago

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le, what percentage of IQ scores are between 77 and 125?

1 answer:

7nadin3 [17] · Answer 1 · 2023-08-18T19:57:01+03:00

3 0

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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