Percentile for total of 20 samples from normal distribution

Steaton

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May 25, 2017
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I need to know how to calculate the distribution of a total based on taking 20 samples from a normal distribution and toitalling them. How much will the total vary? Can I calculate the percentiles for this?

Here is an example:
What is the 90 percentile range for 20 work items with an average cost of £10k with a standard deviation of £4k?
Assuming a normal distribution is reasonable.
The 90th percentile for a single story works out to be between £3.4k and £16.6k (which is quite a big range)
The average cost of all 20 work items would be £200k.
The 90th percentile for all 20 stories is between £X and £Y.

How do I calculate £X and £Y?
 
Are we ALSO assuming the 20 selections are INDEPENDENT? Is the population large enough and the selection methodology sufficient so that we MAY assume Independence? That would make it easier.
 
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