Question

The Wechsler Adult Intelligence Scale (WAIS) is the most common IQ test. The distribution of scores for adults taking the WAIS is approximately Normal with a mean of 100 and a standard deviation of 15. Use the 68–95–99.7 rule to answer the questions about WAIS scores. What percentage of adults score above 100? 32% 84% 50% 2.5% 0.3% 68% What percentage of adults score above 145? 0.15% 0.3% 84% 99.85% 16% 99.7% What percentage of adults score below 85? 99.7% 84% 8% 16% 0.3% 68% Calling itself "the high IQ society," MENSA requires an IQ score of 130 or higher for membership. What percentage of adults taking the WAIS test qualify for membership? (Enter your answer rounded to the nearest tenth of a percent.) percentage:

Answer 1

Answer:

1. 50% 2. 0.15% 3. 16% 4. 2.5%

Step-by-step explanation:

The 68-95-99.7 rule for a mean of 100 and a standard deviation of 15 is shown below.

1. The percentage of adults that score above 100 is 50% because the normal density function is symmetric around its mean, and in this case 100 is the mean, therefore, there are 50% below the mean and 50% above the mean.

2. The percentage of adults that score above 145 is 0.15%, it is easy to verify this using the empirical rule shown below.

3. The percentage of adults scoring below 85 is 16%, i.e., 0.15% + 2.35% + 13.5%

4. The percentage of adults taking the WAIS test that qualify for membership is 2.5%, i.e., 2.35% + 0.15%

Answer 2

Based on the 68–95–99.7 rule, the percentage of adults that scored above 100 is 50%

What is the 68–95–99.7 rule?

The 68–95–99.7 rule is also referred to as the three-sigma rule or the empirical rule and it can be defined as a shorthand that is typically used in statistics to remember the percentage of a population parameter (values) that lie within an interval estimate for a normal distribution.

Basically, the 68–95–99.7 rule states that 68%, 95%, and 99.7% of the population parameter (values) lie within one (1), two (2), and three (3) standard deviations of the mean respectively.

Since the distribution of scores for these adults is approximately normal with a mean of 100, we can deduce the following points:

1. The percentage of adults that scored above 100 is 50% because there are 50% above the mean and 50% below the mean.
2. The percentage of adults that scored above 145 is 0.15% based on the 68–95–99.7 rule.
3. The percentage of adults that scored below 85 is 16% ($0.15 + 2.35 + 13.5$).
4. The percentage of adults that qualify for membership is 2.5% ($2.35+0.15$).

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