Heights of citizens in a large population has a distribution that is symmetric about the mean x

题目

Heights of citizens in a large population has a distribution that is symmetric about the mean x. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is greater than (x − d)?

选项

16%

50%

68%

84%

95%

解析

由于分布关于均值\(x\)对称： - 分布在\((x-d)\)到\(x\)之间的比例，等于分布在\(x\)到\((x+d)\)之间的比例，即\(68\%÷2 = 34\%\) - 同时，分布中大于\(x\)的比例，等于小于\(x\)的比例，均为\(50\%\) 因此，分布中大于\(x-d\)的比例 = 分布在\((x-d)\)到\(x\)之间的比例 + 分布中大于\(x\)的比例 = \(34\% + 50\% = 84\%\)

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