Suppose that IQ scores have a bell-shaped distribution with a mean of 97 and a standard deviation of 17. Using the empirical rul

Question

3 years ago

9

e, what percentage of IQ scores are between 46 and 148

1 answer:

a_sh-v [17] · Answer 1 · 2022-02-25T07:54:07+03:00

Answer:

99.7% of IQ scores are between 46 and 148.

Step-by-step explanation:

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

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

Approximately 95% of the measures are within 2 standard deviations of the mean.

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

In this problem, we have that:

Mean of 97, standard deviation of 17.

What percentage of IQ scores are between 46 and 148?

97 - 3*17 = 46

97 + 3*17 = 148

Within 3 standard deviations of the mean, so:

99.7% of IQ scores are between 46 and 148.