Calculating a Normal Distribution With a Set Mean

Hello,

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:

$5 each

$5.50 each

$7.70 each

$10 each

$11 each

$15 each

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!

Rob

Re: Calculating a Normal Distribution With a Set Mean

Hey Rob636.

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.