Approximately 24% of the calls to an airline reservation phone line result in a reservation being made. (a) Suppose that an operator handles

Question

Approximately 24% of the calls to an airline reservation phone line result in a reservation being made. (a) Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation? (Give the answer to 3 decimal places.)

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Nevaeh 1 day 2021-09-10T09:10:50+00:00 1 Answer 0

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    2021-09-10T09:12:12+00:00

    Answer:

    0.064 = 6.4% probability that none of the 10 calls result in a reservation.

    Step-by-step explanation:

    For each call, there are only two possible outcomes. Either it results in a reservation, or it does not. The probability of a call resulting in a reservation is independent of other calls. So we use the binomial probability distribution to solve this question.

    Binomial probability distribution

    The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    And p is the probability of X happening.

    24% of the calls to an airline reservation phone line result in a reservation being made.

    This means that p = 0.24

    Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?

    This is P(X = 0) when n = 10. So

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    P(X = 0) = C_{10,0}.(0.24)^{0}.(0.76)^{10} = 0.064

    0.064 = 6.4% probability that none of the 10 calls result in a reservation.

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