Calculating a Normal Distribution With a Set Mean
I came across a problem that I was hoping to get some help on.
I have ~$3,260 to spend on 6 different items priced at:
I also need the mean across all items to be equal to ~$8.36.
It doesn't really matter if I'm slightly above, or slightly below the average amount/total amount, but the count of each item has to be a whole number (I can't buy 1/2 a $5 item).
Does anyone know of a formula out there that would allow me to calculate how many of each I require if I assume a normal distribution?
Moreover, something that would be reusable for if I were to have ~$469 to buy the same 6 items where the mean across all items are equal to ~$7.10?
Thank you in advance!
Re: Calculating a Normal Distribution With a Set Mean
You still need to decide what the variance is (to have a specific normal distribution).
Once you do that, then you can calculate the probabilities of "bins" (example: one bin might be $4 - $5) and then use that to describe what the probability of getting certain prices.
To obtain probabilities, you should use a calculator or computer program which should be available after a quick google search. You can also use R which is a free package and use the pnorm command to get probabilities.