Question

The random variable X is normally distributed with mean 9 and standard deviation 0.5. The random variable Y is defined by Y = 3 + 10X. What are the mean and the standard deviation of Y?

A) Mean = 3, Standard Deviation = 10
B) Mean = 13, Standard Deviation = 5
C) Mean = 12, Standard Deviation = 0.5
D) Mean = 9, Standard Deviation = 10

Answer 1

The mean of Y is 93 and the standard deviation of Y is 5.

Step-by-step explanation:

The mean of a random variable Y defined as Y = 3 + 10X is given by the mean of X plus a constant. In this case, the mean of X is 9, so the mean of Y is 3 + (10 * 9) = 3 + 90 = 93.

The standard deviation of a random variable Y defined as Y = 3 + 10X is given by the standard deviation of X times the constant. In this case, the standard deviation of X is 0.5, so the standard deviation of Y is 10 * 0.5 = 5.