Random Variables: Mean and Standard Deviation

[SportsLover]

Homework Statement

The same potato chip company reports that their bags of family sized chips each follows an approx. Normal distribution with a mean of 10.72 ounces and a standard deviation of 0.2 ounces. If the company wants to ship these chips into boxes that contain 6 bags, what would be the mean and standard deviation of the total weight of a box containing 6 bags of chips? The empty boxes have a mean weight of 10 ounces and a standard deviation of 0.05 ounces

Homework Equations

Mean is affected by adding and multiplying
Standard Deviation is only affected by multiplying

The Attempt at a Solution

Mean = 10 +6(10.72)=74.32
Standard Deviation is where I am lost. I thought just 6(.2) but the answer is .493

 

[Orodruin]

The standard variation of the sum of two stochastic variables is not the sum of the standard variations. You neeed to look at the variance.

 

[Ray Vickson]

Homework Statement

The same potato chip company reports that their bags of family sized chips each follows an approx. Normal distribution with a mean of 10.72 ounces and a standard deviation of 0.2 ounces. If the company wants to ship these chips into boxes that contain 6 bags, what would be the mean and standard deviation of the total weight of a box containing 6 bags of chips? The empty boxes have a mean weight of 10 ounces and a standard deviation of 0.05 ounces

Homework Equations

Mean is affected by adding and multiplying
Standard Deviation is only affected by multiplying

The Attempt at a Solution

Mean = 10 +6(10.72)=74.32
Standard Deviation is where I am lost. I thought just 6(.2) but the answer is .493

$$\text{Standard deviation} = \sqrt{\text{Variance}}.$$
What is the variance of a sum of independent random variables?