Question

A variable of two populations has a mean of 42 and a sd of 12 for one of the population (x) and a mean of 36 and a sd of 8 for the other population (y). the variable is normally distributed on each of the two populations. what are the standard deviation (sd) of the distribution of x-y (the difference of two variables)?

Answer 1

The standard deviation of the difference of two variables can be found using the formula sd(x-y) = sqrt(sd(x)^2 + sd(y)^2). Plugging in the values, the standard deviation is approximately 14.42.

Step-by-step explanation:

To find the standard deviation of the difference of two variables (x-y), you can use the formula:

sd(x-y) = sqrt(sd(x)^2 + sd(y)^2)

To find the standard deviation of the difference of two variables we should use the given values. The process is given below;

Plugging in the values, we get sd(x-y) = sqrt(12^2 + 8^2) = sqrt(144 + 64) = sqrt(208) = 14.42

Therefore, the standard deviation of the distribution of x-y is approximately 14.42.