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Math Help - sampling distribution

  1. #1
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    sampling distribution

    In a large city 1 person in 5 is left-handed.
    a. Find the most likely number of left-handed people in a random sample of 6 people.
    b. Find the mean and the standard deviation of the number of left-handed people in a
    random sample of 25 people.
    c. How large must a random sample be if the probability that it contains at least one lefthanded
    person is to be greater than 0.95?
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  2. #2
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    Quote Originally Posted by anonymousgirl View Post
    In a large city 1 person in 5 is left-handed.
    a. Find the most likely number of left-handed people in a random sample of 6 people.
    b. Find the mean and the standard deviation of the number of left-handed people in a
    random sample of 25 people.
    c. How large must a random sample be if the probability that it contains at least one lefthanded
    person is to be greater than 0.95?
    a. Let X be the random variable number of left handed people in a random sample of 6.

    X ~ Binomial (n = 6, p = 1/5)

    E(X) = ..... ?


    b. Let Y be the random variable number of left handed people in a random sample of 25.

    Y ~ Binomial (n = 25, p = 1/5)

    E(Y) = ..... ?

    Var(Y) = .... ?


    c. Let W be the random variable number of left handed people in a random sample of n.

    W ~ Binomial (n = ?, p = 1/5)

    Require the smallest value of n such that

    \Pr(W \geq 1) > 0.95

    \Rightarrow 1 - \Pr(W = 0) > 0.95

    \Rightarrow \Pr(W = 0) < 0.05

    \Rightarrow \left( \frac{4}{5}\right)^n < 0.05.

    Find the smallest value of n that satisfies this inequality.
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    wow tq
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