Question

Suppose that IQ scores have a bell-shaped distribution with a mean of 95 and a standard deviation of 15. Using the empirical rule, what percentage of IQ scores are no more than 65? Please do not round your answer.

Answer 1

Answer:

2.5% of IQ scores are no more than 65

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 = 95

Standard deviation = 15

Using the empirical rule, what percentage of IQ scores are no more than 65?

65 = 95 - 2*15

So 65 is two standard deviations below the mean.

By the Empirical Rule, 95% of the measures are within 2 standard deviation of the mean. Of those 5% which are not, 2.5% are more than 2 standard deviations above the mean and 2.5% are more than 2 standard deviations below the mean.

So 2.5% of IQ scores are no more than 65