Suppose that the number of calories in a veggie burger has m

Suppose that the number of calories in a veggie burger has mean of 400 calories and standard deviation of 12 calories. Suppose that the number of calories in the bun has mean of 100 calories and standard deviation of 5 calories. Suppose that the burger and bun are independent. Find the mean and standard deviation of the total number of calories for a veggie burger and bun (the sum of the two calorie amounts).

The mean is 500 calories and the standard deviation is 169 calories.

The mean is 500 calories and the standard deviation is 13 calories.

The mean is 500 calories and the standard deviation is 17 calories.

The mean is 400 calories and the standard deviation is 13 calories.

The mean is 400 calories and the standard deviation is 17 calories.

Solution

X - Mean in a veggier burger = 400 and sigma = 12

Y - Mean in a bun = 100 and sigma = 5

X and Y are independent.

E(X+Y) = E(x)+E(Y) = 400 +100

= 500 calories

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Var (X+Y) = Var(x) + Var(Y) as x and y are indepdent

= 144+25

= 169

std dev = rt of 169 = 13

The mean is 500 calories and the standard deviation is 13 calories.