Results 1 to 4 of 4

Math Help - Normal approximation to binomial

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    25

    Normal approximation to binomial

    In the following question I know that I am supposed to use the normal approximation to the binomial which we have covered in class but I am not sure how to apply it here.

    It has been statistically determined that 65% of the new chicks of a bird can survive winter. What is the minimum number of chicks to hatch before winter such that there is a 80% probability that at least 6 will survive.


    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by CoraGB View Post
    In the following question I know that I am supposed to use the normal approximation to the binomial which we have covered in class but I am not sure how to apply it here.

    It has been statistically determined that 65% of the new chicks of a bird can survive winter. What is the minimum number of chicks to hatch before winter such that there is a 80% probability that at least 6 will survive.


    Thank you
    Start by defining your random variable: Let X be the random variable number of chicks that survive hatching.

    Define the distribution followed by X: X ~ Binomial(n = ?, p = 0.65).

    Write a probability statement that encapsulates the question: Find the minimum value of n such that \Pr(X \geq 6) \geq 0.8.

    Using trial and error (or, even better, technology) it doesn't take long to get n = 11. I don't see why the normal approximation would be required here.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Thank you Mr. F for your insight into this difficult topic. You are indeed a fine gentelman, and you have helped me a great deal. I'm off to the bus now. I'm very late...

    Regards.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by CoraGB View Post
    In the following question I know that I am supposed to use the normal approximation to the binomial which we have covered in class but I am not sure how to apply it here.

    It has been statistically determined that 65% of the new chicks of a bird can survive winter. What is the minimum number of chicks to hatch before winter such that there is a 80% probability that at least 6 will survive.


    Thank you
    Suppose that N chicks hatch, the number that survive \sim B(N,0.65) , you are asked to find the smallest N so that p(n\ge 6)\ge 0.8 where p(n\ge 6) is that probability that there are 6 or more survivours.

    Using the normal approximation the number of survivours is to be treated as a normal random variable with mean 0.65N and SD \sqrt{N\times0.65\times0.35}.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. normal approximation to the binomial
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 25th 2011, 11:02 AM
  2. Normal approximation to the binomial distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 16th 2010, 03:59 PM
  3. Binomial to Normal Approximation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 15th 2008, 11:04 PM
  4. Statistics Normal to Binomial Approximation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 26th 2008, 08:28 PM
  5. Normal Approximation to the Binomial
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 17th 2008, 02:30 PM

Search Tags


/mathhelpforum @mathhelpforum