Question

a particular iq test is standardized to a normal model, with a mean of 100 and a standard deviation of 10.
a) choose the model for these iq scores that correctly shows what the 68 - 95 - 99.7 rule predicts about the scores.

Explanation:

Step1: Recall the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule for a normal distribution states that approximately 68% of the data lies within \( \mu\pm\sigma\), 95% within \( \mu\pm2\sigma\), and 99.7% within \( \mu\pm3\sigma\).

Step2: Analyze each option

• Option A: The percentages 68% (for \( \mu\pm\sigma\)), 95% (for \( \mu\pm2\sigma\)), and 99.7% (for \( \mu\pm3\sigma\)) are correctly placed.
• Option B: The percentages are mis - placed. The 68% should be for \( \mu\pm\sigma\), not for the outermost interval.
• Option C: The range of values (e.g., starting from 80 instead of 70 when \( \mu = 100\) and \( \sigma=10\)) is incorrect as per the normal distribution centered at \( \mu = 100\) with \( \sigma = 10\).

Answer:

A.