Results 1 to 2 of 2

Math Help - Normal approx to the binomial dist. questions

  1. #1
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303

    Normal approx to the binomial dist. questions

    Q1:

    An airline finds that 5% of the persons who make reservations on a certain flight do not show up for the flight. If the airline sells 160 tickets for a flight with only 155 seats, what is the probability that a seat will be available for every person holding a reservation and planning to fly?

    A1: Let p=0.05, n=160, and W~Normal(np,\sqrt{np(1-p)}.

    Then, P(W\leq\\155.5)=P(\frac{W-np}{\sqrt{np(1-p)}} \leq\frac{155.5-8}{\sqrt{7.6}})

    =P(Z\leq\\53.50, which cannot be correct. The correct answer is 0.898, which I am nowhere close to. Where am I going wrong?

    Q2: (b) A rancom sample of n items is to be selected from a large lot, and the number of defectives Y is to be observed. What value of n guarantees that \frac{Y}{n} will be within .1 of the true fraction of defectives, with probability 0.95?

    Note: Part (a) of this question showed that the variance of \frac{Y}{n}, where Y has a binomial distribution with n trials and success probability of p, has a maximum at p=0.5, which I was able to show.

    A2: Symbolically, I think I need to solve:

    P(|\frac{Y}{n}-p|\leq\\0.1)=0.95, so I want to use the normal approximation to some how come up with a z-value, which I can use to solve for n. Although, when I go down this path I end up with a false equation for n.

    Thanks for you help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Q1: I would venture to guess that the most common error with a binomial distribution is forgetting what we mean by "success". You really just have to write down what you mean. Try p = 0.95. In this way, you will get an expected number of people appearing, not an expected number failing to show up. 53.5 is fine if your are trying to measure to probability of only 8 people appearing at the gate.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. the normal dist
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 27th 2010, 08:18 PM
  2. ahh help please (normal approx. to binomial distribution)
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 26th 2008, 03:09 AM
  3. Proving binomial to approx normal by CLT
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 16th 2008, 01:11 PM
  4. Probability Teaser! Binomial dist or what?
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 19th 2008, 10:03 PM
  5. Normal Dist Prob
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 4th 2007, 06:25 AM

Search Tags


/mathhelpforum @mathhelpforum