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 and. (type integers or decimals. do not round.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 rule

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

Step2: Identify the correct model for part (a)

The correct model should have 68% of the data between $\mu-\sigma$ and $\mu + \sigma$, 95% between $\mu - 2\sigma$ and $\mu+2\sigma$, and 99.7% between $\mu - 3\sigma$ and $\mu + 3\sigma$. Looking at the options, the correct model is the one where the percentages are correctly labeled in these intervals.

Step3: Find the interval for part (b)

For a normal distribution of IQ scores with mean $\mu = 100$ and standard - deviation $\sigma = 15$, the central 68% of the IQ scores are between $\mu-\sigma$ and $\mu+\sigma$. Substituting the values, we get $100 - 15$ and $100+15$.

Answer:

a) The correct model is the one where 68% is between $\mu-\sigma$ and $\mu+\sigma$, 95% is between $\mu - 2\sigma$ and $\mu+2\sigma$, and 99.7% is between $\mu - 3\sigma$ and $\mu + 3\sigma$ (you need to visually check the options to pick the right one).
b) 85, 115