Normal Distribution Problem.

• Sep 6th 2008, 10:42 PM
Firstone
Normal Distribution Problem.
The weights of mandarins in a large crate have a Normal distribution with μ = 110 grams and σ = 16.7 grams. Consider the random process of picking three mandarins independently and putting them in a bag. The standard deviation of the total weight of the three mandarins in the bag is?

Any help would be greatful. =)
• Sep 6th 2008, 11:11 PM
mr fantastic
Quote:

Originally Posted by Firstone
The weights of mandarins in a large crate have a Normal distribution with μ = 110 grams and σ = 16.7 grams. Consider the random process of picking three mandarins independently and putting them in a bag. The standard deviation of the total weight of the three mandarins in the bag is?

Any help would be greatful. =)

Let X be the random variable weight of a single mandarin.
Let Y be the random variable weight of a three mandarins.

Then Y = 3X.

You should know that $\displaystyle \sigma^2_Y = 3^2 \sigma^2_X \Rightarrow \sigma_Y = 3 \sigma_X = \, ....$

In general, if Y = aX + b then $\displaystyle \mu_Y = a \mu_X + b$, $\displaystyle \sigma^2_Y = a^2 \sigma_X^2$ and $\displaystyle \sigma_Y = |a| \sigma_X$.
• Sep 6th 2008, 11:36 PM
Firstone
I'm abit lost in how to do that.

• Sep 7th 2008, 12:28 AM
mr fantastic
Quote:

Originally Posted by Firstone
I'm abit lost in how to do that.

$\displaystyle \sigma_Y = 3 \sigma_x$ and $\displaystyle \sigma_X = 16.7$.