Type of distribution

**gralla55** · May 2nd 2010, 08:34 PM

An air-company estimates the following distributions for the weight of the passangers (attachment), where X is adult males, Y is adult females and B is children.

μ = 85kg and (sigma) = 10kg.

A plane is transporting 108 males, 72 woman and 66 children. What is the expected value and variance for the total weight of all the passangers, and which kind of distribution will it be?

I'm guessing it has something to do with the central limit theorem, and that it will be a normal distribution, but I'm not sure. Any help? Thanks!

**Anonymous1** · May 2nd 2010, 09:15 PM

Theorem. Sum of independent Normals is also normal.

$X$ ~ $N(\mu_ 1, \sigma_1 ^2)$

$Y$ ~ $N(\mu_ 2, \sigma_2 ^2)$

$Z = X+Y$ ~ $N(\mu_ 1 + \mu_ 2, \sigma_1 ^2 + \sigma_2 ^2)$

**gralla55** · May 2nd 2010, 10:17 PM

I figured, but how can I find the variance and expected value?

**Anonymous1** · May 3rd 2010, 05:53 AM

Sum them up... See above.

**gralla55** · May 3rd 2010, 01:07 PM

I'm not sure if that is right... what I'm looking for is the distribution for the "total weight" of these passangers. The distributions I attached is for the distributions of individual passangers.

**Anonymous1** · May 3rd 2010, 02:58 PM

Originally Posted by gralla55

I'm not sure if that is right... what I'm looking for is the distribution for the "total weight" of these passangers. The distributions I attached is for the distributions of individual passangers.

I know what you are looking for. See here:

Normal Sum Distribution -- from Wolfram MathWorld

**gralla55** · May 3rd 2010, 03:39 PM

So if I understand you correctly, this (attachment) should be the right answer?

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