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Math Help - Stats: Multiple Probabilities

  1. #1
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    Question Stats: Multiple Probabilities

    2. Peter is a door-to-door sales representative who makes a sale at only 8% of his house calls. If Peter makes 219 house calls today, what is the probability that:
    (a) he makes a sale at 12 or fewer houses?


    Someone was trying to help me and said 12 x 100/219 = 5.6% but I have no idea where the 100/219 comes into play.

    (b) he makes a sale at 20 or fewer houses?




    (c) he makes a sale at 15 to 25 houses?
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  2. #2
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    Quote Originally Posted by JeanetteR View Post
    2. Peter is a door-to-door sales representative who makes a sale at only 8% of his house calls. If Peter makes 219 house calls today, what is the probability that:
    (a) he makes a sale at 12 or fewer houses?


    Someone was trying to help me and said 12 x 100/219 = 5.6% but I have no idea where the 100/219 comes into play. Mr F says: This is wrong.

    (b) he makes a sale at 20 or fewer houses?




    (c) he makes a sale at 15 to 25 houses?
    Let X be the random variable number of sales made.

    X ~ Binomial(n = 219, p = 0.08)

    (a) Calculate \Pr(X \leq 12).

    (b) Calculate \Pr(X \leq 20).

    A normal approximation to the binomial distribution would be valid here.
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  3. #3
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    For part C

    You have to calculate

    P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) + P(X = 21) + P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)

    X ~ Binomial(n = 219, p = 0.08)
    to find P(x=15) = ( 219 C 15 )(0.08)^15(1-0.08)^204

    Now you have to calculate the rest and add them together.
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