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Binomial distribution problem

  1. Oct 18, 2015 #1
    1. The problem statement, all variables and given/known data

    A company is interested in evaluating its current inspection procedure on large shipments of identical items. The procedure is to take a sample of 5 items and pass the shipment if no more than 1 item is found to be defective. It is known that items are defective at a 10% rate overall.

    (a) What proportion of shipments will be accepted, i.e., what is the probability that the inspection procedure will pass the shipment?

    (b) What is the expected number of defectives in a sample of 5?

    2. Relevant equations
    b(x;n,p) = (nCx) p^x(1-p)^(n-x)
    μ = np

    3. The attempt at a solution
    This is practice for a test and we won't have access to the tables so I need to do this with the formula
    for part a) we are looking for the probability that 0 or 1 item is defective
    this will be
    b(0;5,.1)+b(1;5,.1)
    = (5C0)(.1)^0 (.9)^5 + (5C1)(.1)^1(.9)^4
    = .9^5 + 5(.1)(.9)^4
    = .59049 + .32805
    = .91854

    b) μ = np = 5(.1) = .5

    Am I doing this problem correctly?
     
  2. jcsd
  3. Oct 18, 2015 #2

    ehild

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    Homework Helper
    Gold Member

    Yes.
     
  4. Oct 18, 2015 #3
    thank you
     
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