Question

The mean IQ score of adults is​ 100, with a standard deviation of 15. Use the empirical rule to find the percentage of adults with scores between 70 and 130.​ (Assume the data set has a​ bell-shaped distribution

Answer 1

Answer:

95% of adults with scores between 70 and 130.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution of IQ score is a bell shaped distribution that is a normal distribution.

Empirical Formula:

• According to this rule approximately all the data lies within three standard deviations of mean for a normal distribution.
• About 65% of data lies within one standard deviation of mean.
• About 95% of data lies within two standard deviation of mean.
• About 99.7% of data lies within three standard deviation of mean.

We have to o find the percentage of adults with scores between 70 and 130.

$70 = \mu - 2\sigma = 100 - 2(15)\\130 = \mu + 2\sigma = 100 + 2(15)$

Thus, by Empirical rule, 95% of data lies within two standard deviation of mean, thus, 95% of adults with scores between 70 and 130.