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Need help on simple binomial problem

  1. Jul 13, 2010 #1
    Hello everyone,

    Just have a quick question on a binomial problem.

    The problem is as follows:

    A teacher is giving a 15 question true-false quiz. He wants to design the quiz such that a person that guesses on all the answers have less than a 0.10 probability of passing. What should the teacher put as the passing number of questions to achieve this?

    I have no idea how to do this.
     
  2. jcsd
  3. Jul 13, 2010 #2

    statdad

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    Homework Helper

    Suppose you call the number of correct responses needed to pass [itex] a [/itex]. If [itex] X [/itex] is the number of correc responses from 15 guesses, what must be the relation between [itex] X [/itex] and [itex] a [/itex] in order to pass?
     
  4. Jul 13, 2010 #3
    I have my test in half an hour and that was the only question I didnt know how to do from the review.

    So let A be the number needed to pass, then:

    P(A) = 15_C_A * (0.5)^A * (0.5)^(15-A) = 15_C_A * (0.5)^15 = 0.000030518 * 15_C_A = 0.000030518 * [(15!)/(A!)(15-A)!]

    and since I want P(A) < 0.10 then:

    0.000030518 * [(15!)/(A!)(15-A)!] < 0.10

    and solve for A? (no idea how to solve involving a factorial like that) Is this the way to go about this? A quick response will be appreciated :)
     
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