题目
Let (C) be a random normal variable that characterizes the temperature in degree Celsius. Assume (C) has mean of 30.0 and standard deviation of 2.0. Let (F) be the corresponding temperature in degrees Fahrenheit given by F = 1.8×C + 32. Which of the following statements is the best direct reflection of the location-scale invariance property of the normal distribution?
选项
A.If mean of C were instead 0 with variance of 1, then C would be a standard normal
B.Standard deviation of F is 2.0
C.Standard deviation of F is 3.6
D.F is normally distributed
答案
D
解析
C is a true statement:F = 1.8×C+32;variance(F) = variance(1.8×C + 32) = 1.8^2×variance(C) = 1.8^2×2^2= 12.96 ,standard deviation (F) = √12.96 = 3.6。 So, it is instructive to find the variance of C. However, this does not illustrate the location-scale invariance property of the normal, but rather a simple property of variance.C是正确的: F = 1.8×C+32;variance(F) = variance(1.8×C+ 32) = 1.8^2×variance(C) = 1.8^2×2^2= 12.96 ,standard deviation (F) = √12.96 = 3.6。 因此,找到C的方差是有启发性的。但是,这并没有表明正态分布的位置尺度不变性,而仅是简单的方差性质。