Question

The weight of bags of coffee beans at the grocery store follows a Normal distribution with a mean of μ = 7 ounces and a standard deviation of σ = 2 ounces. Suppose we pick four bags of coffee beans at random from the shelf and find their total weight, W. Which of the following statements describes the random variable W?

A. The random variable W is Normal, with a mean of seven ounces and a standard deviation of two ounces.
B. The random variable W is Normal, with a mean of 28 ounces and a standard deviation of 16 ounces.
C. The random variable W is Normal, with a mean of 28 ounces and a standard deviation of four ounces.
D. The random variable W is binomial, with a mean of 28 ounces and a standard deviation of four ounces.
E. The random variable W is binomial, with a mean of seven ounces and a standard deviation of two ounces.

Answer 1

C.

Explanation:

The random variable W is Normal, with a mean of 28 ounces and a standard deviation of four ounces.

mean of total = 7+7+7+7 = 28

Variance of total = 4+4+4+4 = 16

SD of total = sqrt(16) = 4