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Math Help - tricky statistics question

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    tricky statistics question

    the average for licnesed drivers in the country is an average of 42.6 yrs with a standard deviation of 12. The distribution is approx... normal.
    a. a researcher obtained a sample of n=36 drivers who received parking tickets. The average age for these drivers was m= 40.7. Is this a reasonable outcome for a sample of n=36 or is this sample mean an extreme value?
    b. The same researcher also obtained a sample of n-16. drivers who received speeding tickets. The average for this sample was M=34.4. Is this a reasonable outcome for a sample of n=16 or is the sample mean very different from what would usually be expected? (compute the z-score for the sample mean)
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    Quote Originally Posted by sf415415 View Post
    the average for licnesed drivers in the country is an average of 42.6 yrs with a standard deviation of 12. The distribution is approx... normal.
    a. a researcher obtained a sample of n=36 drivers who received parking tickets. The average age for these drivers was m= 40.7. Is this a reasonable outcome for a sample of n=36 or is this sample mean an extreme value?
    b. The same researcher also obtained a sample of n-16. drivers who received speeding tickets. The average for this sample was M=34.4. Is this a reasonable outcome for a sample of n=16 or is the sample mean very different from what would usually be expected? (compute the z-score for the sample mean)
    Let Y be the random variable sample mean.

    Using a well known result about the sampling distribution of the mean:

    Y ~ Normal \left(\mu = 42.6, ~ \sigma = \frac{12}{\sqrt{n}}\right).

    (a) Calculate \Pr(Y \leq 40.7)

    (b) Calculate \Pr(Y \leq 34.4)

    Calculation of z-scores is done using the formula Z = \frac{Y - \mu}{\sigma}.
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