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Huge Multi Part Prob + Stats question from past paper

  1. Apr 30, 2012 #1
    A university department has 2 secretaries (labelled A and B) who do all the word processing
    required by the department. The number of misprints on a randomly sampled
    page typed by secretary i (i=A,B) has a Poisson distribution with Mean Ui independent
    of the number of misprints on any other page, where Mean Ua = 0.3 and Mean Ub = 1.2.


    Assume that each page is typed entirely by a single secretary. Of the typing required
    by the department, 75% is done by secretary A and 25% by secretary B.


    (a) Find the probability that a randomly sampled page typed by secretary B contains
    more than 1 misprint. [2 marks]


    (b) Calculate the overall proportion of pages produced by the department that contain
    no misprints. [3 marks]


    (c) Suppose that a randomly sampled page produced by the department is found to
    contain 2 misprints. Given this information, calculate the probability that this
    page was typed by secretary A, Hence which secretary is most likely to have typed
    the page concerned? [5 marks]


    A book typed entirely by secretary A consists of 200 pages.
    (i) Let X be the number of pages in the book that contain no misprints. Name
    the (exact) distribution of X. Find approximately the probability that at
    least 150 pages in the book are without misprints. [5 marks]


    (ii) Find approximately the probability that the book contains at most 50 misprints
    in total.


    Attempt At soultions:

    a) Using P(x=K) = (e^-u* u^k)/k! , I get the probability for X=0, X=1 add them and subtract from 1?

    b) 0.25* Prob X=0 from part 1 + same thing for Sec A * 0. 75

    c) Conditional prob. Im happy with this one.

    d) i) I think this is a normal distribution.

    Now if its a normal distribution, mean number of errors per page = 0.3 so number of errors in 200 page will be 60.

    But how do I find The prob of 150+151...200 :S I am very confused and would love some help as my exam is on wednesday!

    Thanks!!
     
    Last edited: Apr 30, 2012
  2. jcsd
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