Valdez Dickson
07/25/2023 · Elementary School
A normal distribution has a mean of 14 and a standard deviation of 4 . Use the 68-95-99.7 rule to find the percentage of values in the distribution above 26. What is the percentage of values in the distribution above 26 ? \( \% \) (Type an integer or a decimal.)
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要解决这个问题，我们需要使用68-95-99.7规则，也称为三西格玛规则。这个规则适用于正态分布，并告诉我们数据在均值（μ）的几个标准差（σ）范围内的百分比。
### 步骤 1：确定已知信息
- 均值（μ）= 14
- 标准差（σ）= 4
### 步骤 2：计算26与均值之间的标准差数
我们需要计算26与均值14之间的标准差数。这可以通过以下公式计算：
\[ \text{标准差数} = \frac{X - \mu}{\sigma} \]
将已知值代入公式：
\[ \text{标准差数} = \frac{26 - 14}{4} = \frac{12}{4} = 3 \]
### 步骤 3：使用68-95-99.7规则
68-95-99.7规则告诉我们：
- 68%的数据在均值的一个标准差范围内
- 95%的数据在均值的两个标准差范围内
- 99.7%的数据在均值的三个标准差范围内
由于26是均值三个标准差之外，我们可以得出以下结论：
- 99.7%的数据在均值三个标准差范围内
- 因此，0.3%的数据在均值三个标准差之外
### 步骤 4：计算高于26的百分比
由于26是均值三个标准差之外，高于26的百分比就是0.3%的数据。
### 最终答案
高于26的百分比是：
\[ 0.3\% \]
所以，高于26的值的百分比是0.3%。
Quick Answer
0.3%
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