Normal Distribution Problem.

**Firstone** · September 6th 2008, 10:42 PM

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. =)

**mr fantastic** · September 6th 2008, 11:11 PM

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 $\sigma^2_Y = 3^2 \sigma^2_X \Rightarrow \sigma_Y = 3 \sigma_X = \, ....$

In general, if Y = aX + b then $\mu_Y = a \mu_X + b$ , $\sigma^2_Y = a^2 \sigma_X^2$ and $\sigma_Y = |a| \sigma_X$ .

**Firstone** · September 6th 2008, 11:36 PM

I'm abit lost in how to do that.

Could someone give me a numeric answer please.

**mr fantastic** · September 7th 2008, 12:28 AM

Originally Posted by Firstone

I'm abit lost in how to do that.

Could someone give me a numeric answer please.

So you've 'progressed' from "Any help would be greatful (sic)" to wanting the whole thing done for you. Sheesh ......

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

Surely you can substitute numbers into a simple formula ....!?

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