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    Question finding Confidence interval without CLT




    Hi all,
    I searched the posts and I did not get what I wanted.
    so here is the question:
    In our Hw we are given daily sales of pastries and coffee for a shop in a semester(which is 70 days). it means I have a mean and a standard deviation for each. Knowing that coffee or pastries are 3$ each, "write a confidence interval for the percentage of sales that comes from pastries, without using the central limit theorem or any other approximation to the normal distribution"

    What I'm not getting is how we can say I am NOt using CLT and what's the matter with each pastry/coffee price?!
    And what does it mean "percentage of sale"?
    May be I'm getting stocked but it makes no sense to me!
    help me pleaaseee!
    If you help me with the concept would be awesome!

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    Re: finding Confidence interval without CLT


    Total sales is number of coffees sold time price of a coffee plus number of pastries sold times price of pastries. Percentage of sales from pastries is sales from pastries divided by total sales. Since the prices are all the same you can just do number of pastries sold divided by ( number of pasties sold plus number of coffees sold). Do you see why? There are several ways of computing a confidence interval for such proportions, some require the CLT others don't. Look at your course notes to see which were discussed in your course/book.

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