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17 June, 05:58

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-through fast-food restaurant is 3 cars in 10 minutes. What is the probability that exactly four cars will arrive in a 5-minute interval?

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  1. 17 June, 06:10
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    You did not state the options to choose from, but I will give a suitable distribution for solving the given problem.

    Answer:

    Poisson Distribution

    Step-by-step explanation:

    Poisson Distributions are used in calculating the probability of an event occurring over a given interval.

    It is calculated using the formula

    P (X = x) = [e^ (-β) β^x]/x!

    Where e = 2.718

    β = mean or expected value of the variable.

    x = number of successes of the event

    Applying this to the given problem, suppose we are trying to find the probability that exactly four cars will arrive in 5 minute interval.

    Average number of cars arriving = 3/10 = 0.3

    The probability of success over a short interval must be the same probability over a long interval, so we have β = 0.3 * 5 = 1.5

    x = 4

    P (X = 4) = [e^ (-1.5) (1.5) ^ (4) ]/4!

    = 0.047066518

    ≈ 0.0047

    There is a 0.47% chance that exactly four cars will arrive in 5 minute interval.
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