The amount of cereal that a manufacturer puts in its boxes of cereal is a random variable with a mean of 1020 g and a standard deviation of 10 g.The amount of cereal that Tyler eats for breakfast is a random variable with a mean of 65 g and a standard deviation of 6 g.The amount of cereal that Tyler's wife,Suzanne,eats for breakfast is a random variable with a mean of 53 g and a standard deviation of 2 g.If Tyler and Suzanne open a new packet of cereal one Monday morning,find the mean and standard deviation of the amount of cereal remaining in the packet after one breakfast.Assume that the amount that Tyler eats is independent of the amount Suzanne eats.
A)μ = 1138 g,σ = 11.83 g
B)μ = 902 g,σ = 11.83 g
C)μ = 1138 g,σ = 2 g
D)μ = 902 g,σ = 7.75 g
E)μ = 902 g,σ = 18 g

Question

Quizplus · Accepted Answer

The amount of cereal remaining in the packet after one breakfast is given by:

X = 1020 g - 65 g - 53 g = 902 g

where X is a random variable representing the amount of cereal remaining.

The mean of X is:

μX = μ1 + μ2 = 1020 g - 65 g - 53 g = 902 g

where μ1 is the mean amount of cereal Tyler eats and μ2 is the mean amount Suzanne eats.

The standard deviation of X is:

σX = sqrt(σ1^2 + σ2^2) = sqrt(10^2 + 6^2 + 2^2) = 11.83 g

where σ1 is the standard deviation of the amount of cereal Tyler eats and σ2 is the standard deviation of the amount Suzanne eats, and we assume the two amounts are independent.

Therefore, the best choice is B.

The Amount of Cereal That a Manufacturer Puts in Its