STATISTICS

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Who is the king of the late night TV? An internet survey estimates that, when given a choice between David Letterman and Jay Leno, 52% of the population prefers to watch Jay Leno. Suppose that you randomly select three late night TV watchers and ask them which of the two talk show hosts they prefer.

a-Find the probability distribution for x, the number of people in the sample of three who would prefer Jay Leno.
b-What is the probability that exactly one of the three would prefer Jay Leno?
c-What are the population mean and standard deviation for the random variable x?

  • STATISTICS -

    Use a normal approximation to the binomial distribution.

    Your values are the following:
    p = .52, q = 1 - p = .48, x = 1, and n = 3

    Find mean and standard deviation.
    mean = np = (3)(.52) = ?
    sd = √npq = √(3)(.52)(.48) = ?

    I'll let you finish the calculations.

    Once you have the mean and standard deviation, use z-scores and z-table to find probability.

    P(0.5 < x < 1.5) =
    P[(0.5 - mean)/sd] < z < [(1.5 - mean)/sd]

    Once you have the two z-scores (substitute the mean and sd calculated), find the difference between the two using a z-table. This will be your probability.

    I hope this will help get you started.

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