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Math Help - Possible Geometric Distribution problem but I'm not sure...

  1. #1
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    Exclamation Possible Geometric Distribution problem but I'm not sure...

    I don't know what formula to use to solve this problem. It sounds like a Geometric Distribution but I'm not sure.

    After repeated observations, it has been determined that the waiting time at the drive-through window of a local bank is skewed left, with a mean of 3.5 minutes and a standard deviation of 1.9 minutes. A random sample of 100 customers is to be taken. What is the probability that the mean of the sample will exceed 4 minutes?

    The answer the teacher provided is 0.0042.

    Thank you.
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  2. #2
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    Re: Possible Geometric Distribution problem but I'm not sure...

    Hey yvonnehr.

    If this is a waiting time that is continuous then you have might want to check the exponential distribution:

    Exponential distribution - Wikipedia, the free encyclopedia
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    Re: Possible Geometric Distribution problem but I'm not sure...

    Quote Originally Posted by yvonnehr View Post
    I don't know what formula to use to solve this problem. It sounds like a Geometric Distribution but I'm not sure.

    After repeated observations, it has been determined that the waiting time at the drive-through window of a local bank is skewed left, with a mean of 3.5 minutes and a standard deviation of 1.9 minutes. A random sample of 100 customers is to be taken. What is the probability that the mean of the sample will exceed 4 minutes?

    The answer the teacher provided is 0.0042.

    Thank you.
    By the Central Limit Theorem, the mean is approximately Normal with mean 3.5 and a standard deviation of \sigma = \frac{1.9}{\sqrt{100}}. (That the waiting time is skewed left is irrelevant.)

    So what is the probability that a Normal random variable with mean 3.5 and standard deviation \sigma (as above) is greater than 4?
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