Suppose that in one town adult men have a mean weight of 77 kg with a standard deviation of 7 kg.Adult women have a mean weight of 63 kg with a standard deviation of 5 kg.10 year old children have a mean weight of 41 kg with a standard deviation of 3 kg.Suppose that a man,a woman,and a 10-year old child get into an elevator.What are the mean and standard deviation of their total weight?
A)μ = 107 kg,σ = 9.11 kg
B)μ = 181 kg,σ = 15 kg
C)μ = 181 kg,σ = 9.11 kg
D)μ = 107 kg,σ = 15 kg
E)μ = 181 kg,σ = 7.33 kg

Question

Quizplus · Accepted Answer

Let's denote the weight of the man, woman, and child as X, Y, and Z respectively. Then, the total weight (W) would be:

W = X + Y + Z

The mean of the total weight would be:

μ = E(W) = E(X+Y+Z) = E(X) + E(Y) + E(Z) = 77 + 63 + 41 = 181 kg

To find the standard deviation of the total weight, we need to use the following formula:

σ(W) = sqrt(σ(X)^2 + σ(Y)^2 + σ(Z)^2)

Plugging in the values, we get:

σ(W) = sqrt(7^2 + 5^2 + 3^2) = sqrt(83) ≈ 9.11 kg

Therefore, the correct answer is choice C.

Suppose That in One Town Adult Men Have a Mean