Question

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 20. Use the empirical rule to determine the following.

(a) What percentage of people has an IQ score between 40 and 160?

(b) What percentage of people has an IQ score less than 60 or greater than 140?

(c) What percentage of people has an IQ score greater than 140?

Answer #1

Given that, mean = 100 and standard deviation = 20

According to Empirical rule,

i) Approximately 68% of the data fall within 1 standard deviations of the mean.

(mean - sd = 100 - 20 = 80 and mean + sd = 100 + 20 = 120)

ii) Approximately 95% of the data fall within 2 standard deviations of the mean.

(mean - 2sd = 100 - (2*20) = 60 and mean + 2sd = 100 + (2*20) = 140)

iii) Approximately 99.7% of the data fall within 3 standard deviations of the mean.

(mean - 3sd = 100 - (3*20) = 40 and mean + 3sd = 100 + (3*20) = 160)

Therefore,

a) **99.7%** of people has an IQ score between 40
and 160.

**Answer : 99.7%**

b) 95% of the people has an IQ score between 60 and 140.

Therefore, 100 - 95 = **5%** of people has an IQ
score less than 60 or greater than 140

**Answer : 5%**

c) 5/2 = **2.5%** of people has an IQ score greater
than 140

**Answer : 2.5%**

Scores of an IQ test have a bell-shaped distribution with a
mean of 100
and a standard deviation of 20.
Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between 40 and
160?
(b) What percentage of people has an IQ score less than 40 or
greater than 160?
(c) What percentage of people has an IQ score greater than
120?

Scores of an IQ test have a bell-shaped distribution with a
mean of 100 and a standard deviation of 20. Use the empirical rule
to determine the following.
(a) What percentage of people has an IQ score between 40 and
160?
(b) What percentage of people has an IQ score less than 80 or
greater than 120?
(c) What percentage of people has an IQ score greater than
160?

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mean of
100
and a standard deviation of
20.
Use the empirical rule to determine the following.
(a) What percentage of people has an IQ score between
80
and
120
(b) What percentage of people has an IQ score less than
40
or greater than
160
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