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Thread: Quick Central Limit Theorem Question

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    Quick Central Limit Theorem Question



    Hi, in this question:
    A cola company that produces cola A claims that consumers prefer their cola to a competitor’s cola, cola B. Suppose 55 % of the cola drinking public prefers cola A to cola B. If the company takes a random sample of 200 cola drinkers, what is the probability that between 54% and 58% of the 200 cola drinkers will prefer cola A to cola B?
    I know the formula to use but since the question asks between 54% and 58% how does that change the formula for the sampling distribution of the sample portion? Thanks

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    Re: Quick Central Limit Theorem Question


    Before you use the CLT to help you, you need to know what exactly the
    question is asking you about.

    Let X be the number of cola drinkers will prefer cola A to cola B
    inside that 200 samples.

    1) What is the distribution of X?

    2)
    the probability that between 54% and 58% of the 200 cola drinkers will prefer cola A to cola B?
    Can you relate the above probability with X ?

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