Question

a) choose the model for these iq scores that correctly shows what the 68 - 95 - 99.7 rule predicts about the scores.
b) in what interval would you expect the central 68% of the iq scores to be found? using the 68 - 95 - 99.7 rule, the central 68% of the iq scores are between 84 and 116. (type integers or decimals. do not round.)
c) about what percent of people should have iq scores above 148? using the 68 - 95 - 99.7 rule, about.15 % of people should have iq scores above 148. (type an integer or a decimal. do not round.)
d) about what percent of people should have iq scores between 68 and 84? using the 68 - 95 - 99.7 rule, about 13.5 % of people should have iq scores between 68 and 84. (type an integer or a decimal. do not round.)
e) about what percent of people should have iq scores above 132? using the 68 - 95 - 99.7 rule, about % of people should have iq scores above 132. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule for a normal distribution states that about 68% of the data is within 1 standard - deviation ($\mu\pm\sigma$) of the mean, about 95% is within 2 standard - deviations ($\mu\pm2\sigma$) of the mean, and about 99.7% is within 3 standard - deviations ($\mu\pm3\sigma$) of the mean.

Step2: Analyze IQ scores distribution

For IQ scores, assume $\mu = 100$ and $\sigma = 16$. So $\mu+\sigma=100 + 16=116$, $\mu - \sigma=100 - 16 = 84$, $\mu+2\sigma=100+32 = 132$, $\mu - 2\sigma=100 - 32 = 68$, $\mu+3\sigma=100 + 48=148$, $\mu - 3\sigma=100 - 48 = 52$.

Step3: Solve part e

The percentage of data within $\mu\pm2\sigma$ is 95%. So the percentage of data outside of $\mu\pm2\sigma$ is $100 - 95=5\%$. This 5% is split evenly between the two tails. So the percentage of data above $\mu + 2\sigma$ (in this case, above 132 since $\mu + 2\sigma=132$) is $\frac{5}{2}=2.5\%$.

Answer:

a) The correct model is the one that shows 68% within $\mu\pm\sigma$, 95% within $\mu\pm2\sigma$, and 99.7% within $\mu\pm3\sigma$. Without seeing the full - fledged options clearly, but based on the rule, the correct distribution should have the percentages labeled correctly as per the rule.
b) 84 and 116
c) 2.5
d) 13.5
e) 2.5