Miguel buys a large bottle and a small bottle of juice.The amount of juice that the manufacturer puts in the large bottle is a random variable with a mean of 1018 ml and a standard deviation of 9 ml.The amount of juice that the manufacturer puts in the small bottle is a random variable with a mean of 506 ml and a standard deviation of 3 ml.Find the mean and standard deviation of the total amount of juice in the two bottles.
A)μ = 1524 ml,σ = 9.49 ml
B)μ = 1136.82 ml,σ = 9.49 ml
C)μ = 1524 ml,σ = 12 ml
D)μ = 512 ml,σ = 12 ml
E)μ = 1524 ml,σ = 90 ml

Question

Quizplus · Accepted Answer

Let X be the amount of juice in the large bottle and Y be the amount of juice in the small bottle. Then, the total amount of juice, Z, is given by Z = X + Y.
The mean of Z is μZ = μX + μY = 1018 ml + 506 ml = 1524 ml.
The variance of Z is Var(Z) = Var(X) + Var(Y) = (9 ml)^2 + (3 ml)^2 = 90 ml^2. So, the standard deviation of Z is σZ = sqrt(Var(Z)) = sqrt(90) ml = 9.49 ml.
Hence, the answer is A.

Miguel Buys a Large Bottle and a Small Bottle of Juice.The