Question

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following.

(a) What percentage of people has an IQ score between 61 and 139?

(b) What percentage of people has an IQ score less than 74 or greater than 126?

(c) What percentage of people has an IQ score greater than 126?

Answer #1

Ans:

Given that

mean=100 and standard deviation=13

**Empirical rule**:

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

a)61 and 139 are **3 standard deviations** below
and above the mean respectively.

So,**99.7%** of the people has an IQ
score between 61 and 139.

**99.7%**

b)74 and 126 are 2 standard deviations below and above the mean respectively.

As,95% of the data falls within 2 standard deviations,so rest
**5%** falls outside these limits.

**5%**

c)126 is 2 standard deviations above the mean.

As 5% falls below and above 2 standard deviations,so half of 5% i.e. 2.5% will fall above 2 standard deviations.

**2.5%**

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