Quantitative Literacy Practice Exam

Where do approximately 99.7% of IQ scores lie if they have a mean of 95 and a standard deviation of 16?

1. Between 50 and 140

2. Between 47 and 143

3. Between 60 and 130

4. Between 70 and 110

The correct answer is: Between 47 and 143

The correct answer is identified based on the application of the empirical rule, also known as the 68-95-99.7 rule, which describes how data is distributed in a normal distribution. The rule states that approximately 68% of observations fall within one standard deviation of the mean, about 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations. In this scenario, the mean IQ score is 95 and the standard deviation is 16. To find the range that captures approximately 99.7% of IQ scores, we need to calculate three standard deviations from the mean. Starting from the mean of 95: - One standard deviation below the mean: 95 - (3 × 16) = 95 - 48 = 47 - One standard deviation above the mean: 95 + (3 × 16) = 95 + 48 = 143 Thus, approximately 99.7% of IQ scores would lie between 47 and 143. Recognizing this range confirms why the chosen option is accurate. Other options provide different ranges that do not encompass the full spectrum of scores expected under the standard deviation calculation, which is why they don't correctly reflect where