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  3. In a normal distribution, the amount of the distribution that lies within 1 stan

In a normal distribution, the amount of the distribution that lies within 1 stan

游客2024-01-12  59
问题 In a normal distribution, the amount of the distribution that lies within 1 standard deviation of the mean is 68 percent, rounded to the nearest whole percent. A certain set of values is normally distributed with a mean of 81 and a standard deviation of 5. A value x will be randomly selected from the set.
Quantity A: The probability that x will be less than 76 or greater than 86
Quantity B: The probability that x will be between 81 and 86
选项 A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.
答案 B
解析 平均值81，标准差为5，小于76或大于86的都在一个标准差以外，由题可知一个标准差以内的占比为68％，故一个标准差以外的占比为32％。根据对称性，81到86之间为0到右边一个标准差，占比为68％的一半即34％，32％＜34％，故答案为B。
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