A level : Statistic

• Theplayfulgirl brainy

  22 Feb 13, 00:21

   Hi, I had a statistic problem. I hope someone will help me.  I only need results for question a and c but I need the solution for b. 

    An office employs two typists, Anniw and Betty. The number of errors Annie and Betty make can be modeled by independent Poisson distribution with means of 0.1 and 0.07 per page respectively.

     a. Betty is given a 200-page document to type. Using a suitable approximation, find the probability that she makes more than 21 errors in the document.

               My answer is : 0.602

     b.  On another occasion, Anniw is given a 10-page document to type while Betty is given a  15-page document to type. Find the probability that the total no of errors in the 2 document is less than 4.

           I have an idea about make some situation to calculate but I guess It must has a better solution

  c. On a thirs occasion, ANnie is given 8 documents to type. Each document consists of 10 pages. Find the probability that at most 2 of the document are error-free

         My answer: 0,433

   

              Thank you

• wee_ws

  22 Feb 13, 08:01

  Hi,

    For (a):
    1. B ~ Po(14) for a 200-page document.
    2. Then B ~ N(14, 14) approximately since mean > 10.
    3. To find P(B > 21) = P(B >= 22), apply continuity correction first.

    For (b):
    1. A ~ Po(1) for a 10-page document and B ~ Po(1.05) for a 15-page document.
    2. Consider A + B ~ Po(2.05), via addition of the means.
    3. Then find P(A + B < 4) = P(A + B <= 3).

    For (c):
    1. A ~ Po(1) for a 10-page document.
    2. Find P(A = 0).
    3. Let X be number of documents, out of 8, that are error-free. Then X follows a binomial distribution.
    4. Find P(X <= 2).

    Thanks.

  Cheers,
  Wen Shih
  wenshih.wordpress.com

• Theplayfulgirl brainy

  22 Feb 13, 17:35

   I got it. Thank you a lot

• Theplayfulgirl brainy

  1 Mar 13, 17:37

    1. the weight of potatoes can be modelled by normal distribution with mean 2400g and standard deviation 6. 

    Prove that the probablitity of weight of 20 potatoes exceeds 5kg is small

  2. There is 95% children took the vaccine. There is 2500 students in sample. 

    X is the probability that they took the vaccine

   Y is  the probability that they not do that

       X or Y can be modelled in Poisson distribution. 

      Find probablity that at least 1295 student took the vaccine by Poisson distributionn

       Someone help me?

• wee_ws

  2 Mar 13, 08:29

  Hi,

    For Q1:

    1. Weight of a potato, X ~ N(2400, 6^2).

    2. Weight of 20 potatoes, X_1 + ... + X_20 ~ N(?, ?).

    3. Use GC to compute P(X_1 + ... + X_20 > 5000) to verify the result.

    Thanks.

  Cheers,
  Wen Shih
  wenshih.wordpress.com

• wee_ws

  2 Mar 13, 08:34

  Hi,

    Please give the full wordings of Q2 because it sounds odd. It is odd because we typically expect the random variable of a Poisson distribution to be some mean value.

    Thanks.

  Cheers,
  Wen Shih
  wenshih.wordpress.com

• Theplayfulgirl brainy

  2 Mar 13, 17:44

    Oh, I'm fucking crazy now. Now, I understand why I did the first question in wrong way. :((((  I should turn 5kg to 5000g but not from g to kg. 
     huhu

• Theplayfulgirl brainy

  2 Mar 13, 17:46

    About second question, I think it is the full question. AK . It is not 1295 but 2495.

   

• wee_ws

  2 Mar 13, 19:41

  Hi,

    I'm afraid Q2 is poorly formulated and is not appropriate for a learner to solve it :P

  Cheers,
  Wen Shih
  wenshih.wordpress.com