Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 17. Using the empirical rule, what percentage of IQ scores are between 87 and 121

Question

Brooke Andrade

Mathematics

6 March, 08:38

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 17. Using the empirical rule, what percentage of IQ scores are between 87 and 121

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Answers (1)

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Elijah Stanton · Answer 1

By the Empirical Rule, 68% of IQ scores are between 87 and 121

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 104

Standard deviation = 17

Using the empirical rule, what percentage of IQ scores are between 87 and 121

87 = 104 - 1*17

So 87 is one standard deviation below the mean

121 = 104 + 1*17

So 121 is one standard deviation above the mean

By the Empirical Rule, 68% of IQ scores are between 87 and 121