1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Probability Finding Binomial Average Problem

  1. Jun 28, 2012 #1
    1. The problem statement, all variables and given/known data

    In each batch of manufactured articles, the proportion of defective articles is p. From each
    batch, a random sample of nine is taken and each of the nine articles is examined. If one article is found to be defective, the batch is rejected; otherwise, it is accepted. If rejected, a second sample of nine is taken and also rejected if an error is found. Otherwise it is accepted.

    Evaluate the average number sampled per manufactured batch over a large number of batches when p has the value 0.1. [4 marks] (Note: Just to be sure you understand what this is asking, you are asked to calculate the average number of articles sampled per manufactured batch over the long run.)

    I condensed the question here is the full incase I worded it poorly:

    In each batch of manufactured articles, the proportion of defective articles is p. From each
    batch, a random sample of nine is taken and each of the nine articles is examined. If two
    or more of the nine articles are found to be defective, the batch is rejected; otherwise, it
    is accepted. Show that the probability that a batch is accepted is (1−p)
    8
    (1+8p). [3 marks]
    It is decided to modify the sampling scheme so that when one defective is found in the
    sample, a second sample of nine is taken (each of the nine articles is examined) and the
    batch rejected if this contains any defectives. With this exception, the original scheme is
    continued. Find an expression in terms of p for the probability that a batch is accepted.
    [3 marks].
    For this modified scheme, evaluate the average number sampled per manufactured batch
    over a large number of batches when p has the value 0.1. [4 marks] (Note: Just to be
    sure you understand what this is asking, you are asked to calculate the average number of
    articles sampled per manufactured batch over the long run.)
    Attempt:
    Any hints on the process?

    My guess:

    The probability for the # of error is easy using binomials.

    It's discrete binomial question so I was thinking about making a table to find E(X) where X = # of error,

    average # error = E(X) = X1*P1 + X2*P2 .... X18*P18 , 18 since 2 samples and professor hint was answer is between 9 - 18.

    E(X) = np since binomial, where n = 18?
    E(X) / p = n , which is the answer?

    Thanks for any help.
     
    Last edited: Jun 28, 2012
  2. jcsd
  3. Jun 28, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Do you mean "at least one"?

    What happens if the batch is rejected a second time? Do you do only one or two samples?

     
  4. Jun 28, 2012 #3
    Sorry I meant at least one. I was a little confused on the initial wording too, but I believe it is a max of two samples.
     
  5. Jun 28, 2012 #4
    I see someone else is also doing the STAT 251 HW late. :tongue:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Probability Finding Binomial Average Problem
  1. Binomial Probabilities (Replies: 2)

Loading...