ExplanationWhenever the words “Normal distribution” appear on the GRE, draw a bell-curve diagram that approximates the one below. Memorize the numbers 34 : 14 : 2.
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The middle of the bell curve is the average, or mean, so place 5.2 underneath the 0 in the center; 34%, 14%, and 2% represent the approximate percentages that fall between the standard deviation lines.
For instance, 14% of the population falls between 1 and 2 standard deviations below the mean. Now, use the standard deviation of 0.6 grams to figure out the exact dividing lines between the marked regions of the normal curve. The mass of an insect that is exactly 1 standard deviation above the mean is 5.2 + 0.6 = 5.8, and the mass of one that is 1 standard deviation below the mean is 5.2 – 0.6 = 4.6.
Similarly, the mass at exactly 2 standard deviations above the mean is 6.4 and at 2 below is 4.0.
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Quantity A, the percent between 5.2 and 5.8 grams, is 34%.
However, Quantity B will require some estimating. Note that 4.9 is halfway between 4.6 and 5.2, while 5.5 is halfway between 5.2 and 5.8. Therefore, the area between 4.9 and 5.5, while still a range of 0.6, is under the bigger part of the bell curve in the center. Since the area under the center is bigger than the area between 0 and 1 standard deviations, the percentage of the area under the center must also be greater. Therefore, Quantity B is greater.
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