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A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 17.

a) Choose the model for these IQ scores that correctly shows what the 68-95-99.7 rule predicts about the scores.

b) In what interval would you expect the central 68% of the IQ scores to be found?
Using the 68-95-99.7 rule, the central 68% of the IQ scores are between ____ and ____. (Type integers or decimals. Do not round.)

c) About what percent of people should have IQ scores above 134?
Using the 68-95-99.7 rule, about ____% of people should have IQ scores above 134. (Type an integer or decimal. Do not round.)

d) About what percent of people should have IQ scores between 83 and 100?
Using the 68-95-99.7 rule, about ____% of people should have IQ scores between 83 and 100. (Type an integer or decimal. Do not round.)

e) About what percent of people should have IQ scores above 151?
Using the 68-95-99.7 rule, about ____% of people should have IQ scores above 151. (Type an integer or decimal. Do not round.)

Answer :

Final answer:

According to the empirical rule (68-95-99.7 rule), approximately 68% of IQ scores will fall between 83 and 117, 2.5% of people will have scores above 134, and less than 0.15% will have scores above 151. Approximately 34% will have scores between 83 and 100.

Explanation:

The model to show the 68-95-99.7 rule about the IQ scores is a Normal distribution with a mean of 100 and standard deviation of 17. This rule is also known as the empirical rule, stating that approximately 68% of the values lie within one standard deviation of the mean, 95% within two standard deviations and 99.7% within three standard deviations.

To find the interval where the central 68% of IQ scores would be, we simply add and subtract the value of the standard deviation from the mean. This gives us an interval of (100-17) = 83 and (100+17) = 117 for the IQ scores.

In the context of the 68-95-99.7 rule, if we want to find the percent of people who have IQ scores above 134, this puts us in the area above one standard deviation beyond the mean. Looking at the rule, about 16% (half of the remaining 32% outside the first standard deviation) have scores above 117, and 2.5% (half of the remaining 5% beyond two standard deviations) will have scores above 134.

When we look again at this standard distribution for the percentage of people who should have IQ scores between 83 and 100, we see that this includes all scores within half of the first standard deviation, which is 34% of people.

Finally, to determine the percentage of people with IQs above 151, we can recall that this is more than three standard deviations above the mean, hence less than 0.15% of people (half of the remaining 0.3% beyond the third standard deviation) are expected to have IQ scores above 151.

Learn more about Empirical Rule here:

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