Multiple choice

For a certain dataset, the measurement 15.2 is 2.0 standard deviations below the mean, and the measurement 19.6 is 3.5 standard deviations above the mean. Quantity A The mean of the dataset Quantity B 16.5

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M be the mean and S be the standard deviation. 15.2 = M - 2S and 19.6 = M + 3.5S. Subtracting the equations: 4.4 = 5.5S, so S = 0.8. Then M = 15.2 + 2(0.8) = 15.2 + 1.6 = 16.8. Since 16.8 > 16.5, Quantity A is greater.

AI explanation

Using the standard score formula, we get two equations: mean minus 2.0 standard deviations equals 15.2, and mean plus 3.5 standard deviations equals 19.6. Subtracting the first equation from the second gives 5.5 standard deviations equals 4.4, meaning one standard deviation is 0.8. Substituting this back into the first equation gives a mean of 15.2 plus 1.6, which is 16.8. Since 16.8 is greater than 16.5, Quantity A is greater.

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