Multiple choice

There are eight numbers in a set: 9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5. The mean and the standard deviation of these eight numbers are 10.0 and 0.3, respectively. What percent of the eight numbers are within 1 standard deviation of the mean?

  1. 25%

  2. 37.5%

  3. 50%

  4. 75%

  5. 62.5%
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D Correct answer
Explanation

Mean = 10.0, SD = 0.3. Range = [9.7, 10.3]. Numbers within this range: 9.9, 9.9, 9.9, 10.0, 10.2, 10.2. Total = 6 numbers. 6/8 = 75%.

AI explanation

To find the values within one standard deviation of the mean, calculate the interval by subtracting and adding the standard deviation of 0.3 to the mean of 10.0, giving a range of 9.7 to 10.3. Six of the eight numbers (9.9, 9.9, 9.9, 10.0, 10.2, 10.2) fall within this range. The percentage is calculated as 6 divided by 8, multiplied by 100, which equals 75%.

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