Results 1 to 6 of 6

Math Help - Statistics Special Distributions

  1. #1
    Member
    Joined
    Nov 2013
    From
    Philadelphia
    Posts
    169

    Statistics Special Distributions

    1.

    A plan for an executive travelers' club has been developed by an
    airline on the premise that 15% of its current customers would
    qualify for membership.



    a.)
    Assuming the validity of this premise, among 25 randomly selected
    current customers, what is the probability that exactly 2
    qualify for membership?

    Assuming the validity of this premise, among 25 randomly selected
    current customers, what is the probability that at least 2
    qualify for membership?

    b.)
    Again assuming the validity of the premise, what are the expected
    number of customers who qualify and the standard deviation of the
    number who qualify in a random sample of 25 current customers?

    c.)

    Let X denote the number in a random sample of 25 current customers
    who qualify for membership. Consider rejecting the company's premise
    in favor of the claim that more than 15% qualify if X >= 7.

    What is the probability that the company's premise is rejected
    when it is actually valid?

    What is the probability that the company's premise is rejected
    when in reality 20% qualify?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,698
    Thanks
    620

    Re: Statistics Special Distributions

    Hey AwesomeHedgehog.

    The first thing you need to do in these kinds of questions is either choose or create a statistical model. If you have a situation of success or failure repeated n times (where they are all independent) then you have a Binomial distribution (big hint). See if you can use this information to do your questions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2013
    From
    Philadelphia
    Posts
    169

    Re: Statistics Special Distributions

    Hey,
    I got parts a and b.

    For part a, I got:
    b(2; 25, 15) = (25C2)*((0.15)^2)*(1-0.15)^23 = 0.161

    P(X >= 2) = 1 - P(X < 2) = 1 - [P(X = 1) + P(X = 0)] = 0.906

    For part b, I got:

    E(X) = 25 * 0.15 = 3.75

    Var(X) = 25 * 0.15 * (1 - 015) = 3.1875

    sqrt(3.1875) = 1.785 = stdev

    The only problem I'm having now is part c.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,698
    Thanks
    620

    Re: Statistics Special Distributions

    Have you studied conditional probability? (P(A|B) = P(A and B)/P(B)). If so how do you understand it? (This is a direct application of conditional probability).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2013
    From
    Philadelphia
    Posts
    169

    Re: Statistics Special Distributions

    I do not understand how that applies to part c.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,698
    Thanks
    620

    Re: Statistics Special Distributions

    You are looking at P(Reject Premise|Valid) and P(Reject|20% Qualify).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 6th 2013, 10:29 AM
  2. Looking for special polynomials
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: July 6th 2010, 08:48 AM
  3. Special Relativity #2
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: December 7th 2009, 01:47 PM
  4. Replies: 6
    Last Post: January 16th 2009, 04:15 AM
  5. special e
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 22nd 2007, 01:31 PM

Search Tags


/mathhelpforum @mathhelpforum