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.

BUSI_V 291 202 2024W2 Ch 07 Quiz Level 1

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

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BUSI_V 291 202 2024W2 Ch 07 Quiz Level 1

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

查看解析

登录即可查看完整答案

类似问题

Suppose a population has probability distribution with a mean 𝜇 and a standard deviation 𝜎 . If a random sample of 100 measurements are taken from this population, you would expect very few of them to fall within 3 standard deviations of the mean. c07.p066.q001

The Empirical Rule states that for a bell-shaped distribution, approximately 95 percent of data should lie within:

According to the Empirical​ Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about

Empirical Rule Q3 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

Empirical Rule Q3 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

Empirical Rule Q3 a) What is the numerical value for the lower bound (LB) of the interval? Enter your answer as a whole number.

Empirical Rule Q2 d) Find P(LB < Z< UB). Enter your answer to 4 decimal places.

Empirical Rule Q2 b) What is the numerical value for the upper bound (UB) of the interval? Enter your answer as a whole number.

更多留学生实用工具

希望你的学习变得更简单

According to the Empirical Rule, the probability that a selected dog of this breed weighs more than 161 pounds is about