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StatisticsQ&A LibraryScores of An IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following.a) What percentage of people has an IQ score between 88 and 112?b) what percentage of people has an IQ score less than 76 or greater than 124?c) what percentage of people has an IQ score greater than 134?Question

Asked Jan 16, 2020

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Scores of An IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rule to determine the following.

a) What percentage of people has an IQ score between 88 and 112?

b) what percentage of people has an IQ score less than 76 or greater than 124?

c) what percentage of people has an IQ score greater than 134?

Step 1

**Empirical Rule for normal distribution:**

- The percentage of values lies between one standard deviation from the mean is 68%.
- The percentage of values lies between two standard deviation from the mean is 95%.
- The percentage of values lies between one standard deviation from the mean is 99.7%

Step 2

a)

The percentage of people has an IQ score between 88 and 112 is ** 68%** and it is obtained below:

From the given information, the scores of an IQ test have a bell-shaped distribution with mean of 100 and a standard deviation of 12.

Step 3

That is, the given two values representing the one standard deviation from the mean.

Hence, the percentage of people has an IQ score between 88 and 112 is **68%**.

b)

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