Question

A random variable X has a mean of 120 and a standard deviation of 15 a random variable Y has a mean of 100 and a standard deviation of 9. if c and y are independent approximately what is the standard deviation of X plus Y

Answer 1

Answer:

The standard deviation is 17.5

Step-by-step explanation:

Let S be the sum of X and Y

S = X + Y

So we want to calculate the standard deviation of S

The standard deviation of S will be the square root of the sum of the variances of X and Y

Kindly recall that variance is the square of standard deviation

The variance of X will be 15^2 = 225

The variance of Y will be 9^2 = 81

So the standard deviation of the sum will be

√(81 + 225)

= √(306)

= 17.5