ExplanationNormal distributions are always centered on and symmetrical around the mean, so the chance that the worm’s length will be within a certain 6-centimeter range (or any specific range) is highest when that range is centered on the mean, which in this case is 30 centimeters.
More specifically, Quantity A equals the area between –2 standard deviations and the mean of the distribution. In a normal distribution, roughly 34 + 34 + 14 + 14 = 96% of the sample will fall within 2 standard deviations above or below the mean. Limit yourself only to the 2 standard deviations below the mean, then half of that, or 96%÷2 = 48%, falls in this range. In contrast, Quantity B equals the area between –1 standard deviation and +1 standard deviation. In a normal distribution, roughly 34 + 34 = 68% of the sample falls within 1 standard deviation above or below the mean. Since 68% is greater than 48%, Quantity B is greater.
Note that exact figures are not required to answer this question! Picture any bell curve—the area under the “hump” (that is, centered around the middle) is bigger! Thus, it has more members of the dataset (in this case, worms) in it.
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