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    Records indicate that 70 percent of Canadians submit their income tax returns by March 31 of each year when required to do so. In a random sample of 10 Canadians who are required to submit income tax returns,

    A) What is the probability that 9 or more will submit their return by March 31?
    B) What is the probability that exactly 5 will have submitted their return by March 31?

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/probability-calculations-binomial-distribution-15391

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    SOLUTION This solution is FREE courtesy of BrainMass!

    p= 0.7 or 70.00% (70% of Canadians submit their income tax returns by March 31)
    q=1-p 0.3 or 30.00% (remaining 30% of Canadians do not submit their income tax returns by March 31)

    This is a Binomial distribution

    A) What is the probability that 9 or more will submit their return by March 31?

    Probability that 9 or more will submit their return by March 31=
    Probability that 9 will submit returns+ Probability that 10 will submit return)

    Probability that 9 will submit returns=

    p= 0.7
    q=1-p= 0.3
    n= 10
    r= 9

    P(r)= ncr p r * q 1-r

    Therefore

    P(r)= ncr p r * q n-r = =10*(0.7^9)*(0.3^1)
    = 0.121060821 or 12.10608%

    Probability that 10 will submit returns=

    p= 0.7
    q=1-p= 0.3
    n= 10
    r= 10

    P(r)= ncr p r * q 1-r

    Therefore

    P(r)= ncr p r * q n-r = =1*(0.7^10)*(0.3^0)
    = 0.0282475 or 2.82475%

    Therefore Probability that 9 or more will submit their return by March 31=
    =
    Probability that 9 will submit returns + Probability that 10 will submit return
    = 0.1493083 or 14.93084%
    =0.1211+0.0282

    Answer: 0.1493 or 14.93%

    B) What is the probability that exactly 5 will have submitted their return by March 31?

    Probability that 0 will submit returns =

    p= 0.7
    q=1-p= 0.3
    n= 10
    r= 5

    P(r)= ncr p r * q 1-r

    Therefore

    P(r)= ncr p r * q n-r = =252*(0.7^5)*(0.3^5)
    = 0.102919345 or 10.29194%

    Answer: 0.102919345 or 10.29194%

    See attached file too

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf>
    https://brainmass.com/statistics/probability/probability-calculations-binomial-distribution-15391

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