Using the 68-95-99.7 rule, about 16 % of people should have IQ scores above 117.

Question

BlackTom AI · Accepted Answer

The question asks us to evaluate a claim using the 68-95-99.7 rule.

First, recall the standard IQ distribution is approximately normal with a mean of 100 and a standard deviation of 15.

Compute the z-score for 117: z = (117 - 100) / 15 ≈ 1.133.

Interpretation of the normal curve: about 84% of people fall at or below +1 standard deviation, and about 16% fall above +1 standard deviation. However, this 16% corresponds to thresholds at roughly 115 (since 100 + 1*15 = 115), not 117.

Next, determine the proportion above 117 by looking at z > 1.133. The tail probability beyond z = 1.133 is approximately 0.129 or about 12.9%, which is closer to 13% rather than 16%. The exact value depends on the standard normal CDF, but the key point is that 117 lies to the right of the +1 SD mark (115), and thus the tail beyond 117 is smaller than the 16% associated with a threshold of 115.

Therefore, the stated figure of about 16% of people scoring above 117 does not align with the 68-95-99.7 rule when applied to a normal IQ distribution with mean 100 and SD 15.

In summary, using the rule and standard normal calculations, the percentage above 117 is less than 16% (approximately 13%), so the claim is not accurate.

Using the 68-95-99.7 rule, about 16 % of people should have IQ scores above 117.Multiple dropdown selections

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