suppose I've sampled 6 numbers from a popluation...

• Nov 13th 2012, 11:59 AM
datanewb
suppose I've sampled 6 numbers from a popluation...
Suppose I've sampled 6 numbers from a population: 25,26,26,27,28,29.

In that case $\displaystyle \mu = 26.833$ and $\displaystyle \sigma = 1.47196$.

How can I calculate the likelihood that the next three numbers will sum to say 90 or more?
• Nov 13th 2012, 08:03 PM
chiro
Re: suppose I've sampled 6 numbers from a popluation...
Hey datanewb.

For this you will need to assume a distribution for the population and calculate the probability P(X1 + X2 + X3 > 90|Previous Observations). If you assume I.I.D samples then you will just calculate P(X1 + X2 + X3 > 90).

Did you have a distribution in mind?
• Nov 14th 2012, 09:07 AM
datanewb
Re: suppose I've sampled 6 numbers from a popluation...
chiro, thank you for getting me on the right track! I expected for there to be a mathematical formula I could just plug into, but now I see there are quite a few assumptions necessary to make such a calculation. I suppose I will just assume a normal distribution, although from the posted histogram, you can see that it doesn't exactly look normal. There are actually 90 data points involved (not 6 as the original question stated).Attachment 25715