Multiple choice

9.4, 9.9, 9.9, 9.9, 10.0, 10.2, 10.2, 10.5 The mean and the standard deviation of the 8 numbers shown are 10 and 0.3, respectively. What percentage of the 8 number's are within 1 standard deviation?

  1. 90%

  2. 85%

  3. 80%

  4. 75%

  5. 70%
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D Correct answer
Explanation

One standard deviation from the mean gives the interval 10 - 0.3 to 10 + 0.3, or 9.7 to 10.3. Six values lie in this interval, while 9.4 and 10.5 do not. Thus, the percentage is 6/8 x 100 = 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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