- Thread starter x46949
- Start date

I am going to assume you mean the sum of multiple normally distributed random variables. In that case you need to look into the Normal sum distribution.

SCE1000 said:

If you have two distributions with wildly different means, and very tight standard deviations, why would you get another normal distribution?

@hlsmith - I'm not sure what you were asking exactly.

Trying to wrap my head around if they would be colinear or not. Or what types of scales or units they may have.

Also trying to picture how two variables might be uncorrelated and how their sums would look normal. Say I have heights and I am adding it to some made up variable where those with centrally located heights had extremes values on the other variable. An example would help me understand how in this scenario the sum would be normal. I get the addition of correlated variables but don't intuitive get the sum of two totally different scales.

Let's say a different normal curve describes each of the following activities, in minutes: how long it takes to drive to the dentist (mean=5, stdev=2), how long I spend there (60, 15), and how long it takes to drive back home, fighting traffic (15, 5).

If I wanted to know with 95% confidence that I had allocated enough time in my schedule to accommodate the total trip, how would I find the value of the joint distribution at +2 standard deviations?

This is a simplified but relevant example of what I'm trying to solve, and I think it's in the spirit of the OP's question. Thanks in advance for any help!