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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
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2024-01-12
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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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