Quote:
Originally Posted by DanT
Hi Fat Elvis,
The problem involves a discrete distribution that puts 25% probability on each of the integers from 1 to 4. The course materials should have provided you a formula for computing the standard deviation for such a distribution, right? If you were to plot the density of that distribution, you will see that it looks nothing like a normal curve. Instead, the distribution puts the same amount of weight on each of only 4 points. You can compute the standard deviation for the problem's discrete uniform distribution using the formula you have for a standard deviation for a discrete probability distribution. (Alternatively, you can simply use one of the two Excel's functions for calculating POPULATION standard deviations and apply that to the four integers, like this:
=stdevp(1,2,3,4)
)
If you do that, you will learn what the population standard deviation is for that distribution. Once you know that, then you just need to compute what 2.57 of those standard deviations would equal. Then you just need to find the next greatest integer, aka the ceiling, aka the minimum integer whose value is at least as big as 2.57 * SD, where SD is the standard deviation whose value you computed at the beginning of the problem.
If I'm interpreting that problem correctly, I suspect that the intent of the problem is to help the student get familiar with translating a word problem into a math problem and then apply concepts you learned early in the class about standard deviations and other parameters that describe key features of distributions.
Hope this helps gets you started on the other problems!
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DanT-
I really appreciate your help. It was late last night (late for me), so I really wasn't expressing myself very clearly. I'm not in a class now, and it has been over 25 years since I've taken a stats/probability class, so I've forgotten most everything. I think that is why the wording is pretty wonky. I was just looking at some old D&D dice that I had stumbled across while working in the basement, and for some reason it had me thinking about stats and probability. I think I worded things the way that I had because, in my mind, I was trying to generalize the concepts beyond the die/dice.
Perhaps you can clear some things up for me since my addled brain is a bit foggy. Lets assume that an event has a .25 probability of occuring; would the population size affect the mean and standard deviation? Perhaps it only affects variance? The smaller the population size, the greater the variance? This would be due to the Central Limit Theorem, correct?
I think Third Eye was getting what I was asking; I just did a poor job of asking the question. I have more questions though; I just need to relearn how to crawl before I start walking again with this....