NO.PZ2022062760000024
问题如下:
Assume that a random variable X follows a normal distribution with a mean of 40 and a standard deviation of 14. What is the probability that X does not lie between 12 and 61?
选项:
A.
4.56%
B.
6.18%
C.
8.96%
D.
18.15%
解释:
中文解析:
首先标准化X,当X=12和61时,利用公式:
查表得出概率:
𝑃(𝑧 < −2) = 0.0228
𝑃(𝑧 > 1.5) = 0.0668
那么𝑃(𝑧 < −2) or 𝑃(𝑧 > 1.5) = 0.0228 + 0.0668 = 0.0896.
First we must find the standardized (z) values for 12 and 61.
Next, using a Z table we find the probability that z is less than -2:
𝑃(𝑧 < −2) = 0.0228
And we find the probability that z is greater than 1.5:
𝑃(𝑧 > 1.5) = 0.0668
Finally we add these values to find the probability that z is less than -2 or greater than 1.5:
𝑃(𝑧 < −2) or 𝑃(𝑧 > 1.5) = 0.0228 + 0.0668 = 0.0896.
感觉不是很严谨,考试时该怎么区分