Questions: Part 3 of 5 Points: 0 of 1 A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 13. a) Choose the model for these IQ scores that correctly shows what the 68-95-99.7 rule predicts about the scores. A. B. C. 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 87 and 113. (Type integers or decimals. Do not round.) c) About what percent of people should have IQ scores above 126? Using the 68-95-99.7 rule, about % of people should have IQ scores above 126. (Type an integer or a decimal. Do not round.)

Part 3 of 5 Points: 0 of 1

A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 13. a) Choose the model for these IQ scores that correctly shows what the 68-95-99.7 rule predicts about the scores. A. B. C. 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 87 and 113. (Type integers or decimals. Do not round.) c) About what percent of people should have IQ scores above 126?

Using the 68-95-99.7 rule, about % of people should have IQ scores above 126. (Type an integer or a decimal. Do not round.)

Transcript text: Part 3 of 5 Points: 0 of 1 A particular IQ test is standardized to a Normal model, with a mean of 100 and a standard deviation of 13 . a) Choose the model for these IQ scores that correctly shows what the 68-95-99.7 rule predicts about the scores. A. B. C. 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 87 and 113. (Type integers or decimals. Do not round.) c) About what percent of people should have IQ scores above $126 ?$ Using the 68-95-99.7 rule, about $\square \%$ of people should have IQ scores above 126. (Type an integer or a decimal. Do not round.)

Solution

Solution Steps

Step 1: Choose the correct model

The 68-95-99.7 rule states that for a normal distribution:

68% of the data falls within 1 standard deviation of the mean.
95% of the data falls within 2 standard deviations of the mean.
99.7% of the data falls within 3 standard deviations of the mean.

The correct model that shows this rule is A.

Step 2: Determine the interval for the central 68% of IQ scores

The mean (μ) is 100 and the standard deviation (σ) is 13. According to the 68-95-99.7 rule, 68% of the data falls within 1 standard deviation of the mean.

\[ \text{Interval} = \mu \pm \sigma \] \[ \text{Interval} = 100 \pm 13 \] \[ \text{Interval} = (87, 113) \]

Step 3: Calculate the percentage of people with IQ scores above 126

Using the 68-95-99.7 rule, 126 is 2 standard deviations above the mean (100 + 2*13 = 126).

95% of the data falls within 2 standard deviations (between 74 and 126).
Therefore, 5% of the data falls outside this range.
Since the normal distribution is symmetric, half of this 5% (2.5%) falls above 126.