Probably very easy.

#1
For the past year, I have spent about 4.00$ a day for lunch, give or take a quarter or so.

(a) draw a rough sketch of this distribution of daily expenditures
(b) if, without looking at the bill, I paid for my lunch with a 5$ bill and recieved 0.75$ in change, should I worry that i was overcharged
(c) explain logic in part (b)

okay I know this has to do with a sampling distribution of some sort. I just have no idea how to setup/approach the question. can someone get me started?
 
#2
Sounds like a normal distribution problem. Of course the mean would be $4. The stated information "give or take a quarter or so" sounds like 2 standard deviations would be $0.25, since for a normal distribution 95.45% of the data lies within 2 standard deviations of the mean (plus and minus two SDs). So the standard deviation would be $0.125.

To answer part (b), I'd convert the amount paid ($4.25) into a z score. This will tell you how many SDs above or below the mean $4.25 is. You should get 2. That means it's at the border between being within 2 standard deviations of the mean and being outside. Now it's up to you to decide if that amount is surprising or not.
 
#3
P ( z > +2 ) = 0.0228 or 2.28%

I know this is in the extreme region ( extreme right tail ). If I was doing a hypothesis test, I would conclude for example this is a statistical significant effect (at alpha = 0.05). How do I translate this into what the question is asking? I know this is 'not likely due to chance' meaning I was overcharged?
 
#4
The only problem is, z=2, so it isn't z>2. It's true that P(z>2) = P(z>=2) so you could count it as out of the ordinary. But on the other hand P(-2<z<2) = P(-2<=z<=2) so you could also count it as ordinary.
I suspect the person who set the question would be happy either way, if you explain your reasoning in part (c) of the problem.
 
#5
ahh cool thanks for the help! just a side question, do you find the structure/wording of the problem a bit vague / unclear at all? We're using this new text for intermediate stats and while the chapters are easy to read, the questions seem so unorthodox , relative to what we've had before in statistics for behavioral sciences..
 
#6
Yeah, this question seems a bit vague...it'd be nice if the question mentioned that you can assume normally-distributed prices, and also that $0.25 is two standard deviations. I guess they're trying to make you independently come up with the assumptions (maybe this is easier if you see which chapter the exercise is attached to and the topic of that chapter).