Sue buys a large packet of rice.The amount of rice that the manufacturer puts in the packet is a random variable with a mean of 1022 g and a standard deviation of 11 g.The amount of rice that Sue uses in a week has a mean of 240 g and a standard deviation of 26 g.Find the mean and standard deviation of the amount of rice remaining in the packet after a week.
A)μ = 1262 g,σ = 37 g
B)μ = 782 g,σ = 23.56 g
C)μ = 782 g,σ = 28.23 g
D)μ = 782 g,σ = 15 g
E)μ = 1262 g,σ = 28.23 g

Question

Quizplus · Accepted Answer

Let X be the amount of rice in the packet and Y be the amount of rice used in a week. Then,
E(Y) = 240 g
σ(Y) = 26 g
E(X) = 1022 g
σ(X) = 11 g
We need to find E(X-Y) and σ(X-Y).
E(X-Y) = E(X) - E(Y) = 1022 - 240 = 782 g
σ(X-Y) = sqrt(σ(X)^2 + σ(Y)^2) = sqrt((11)^2 + (26)^2) = 28.23 g

Therefore, the answer is C.

Sue Buys a Large Packet of Rice