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2 March, 03:23

Consider an espresso stand with a single barista. Customers arrive to the stand at the rate of 28 per hour according to a Poisson distribution. Service times are exponentially distributed with a service rate of 35 customers per hour. The probability that there are exactly 3 customers in the system is Group of answer choices

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  1. 2 March, 06:01
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    The probability that there are exactly 3 customers in the system is 0.1024

    Explanation:

    Arrival rate (λ) = 28 customers/hour

    Service rate (μ) = 35 customers/hour

    Proportion of busy time of the server (ρ) = λ/μ

    ρ = 28/35 = 0.8

    Probability that there are exactly 3 customers in the system

    (P₃) = ρ³ (1 - ρ)

    P₃ = 0.8³ (1 - 0.8)

    P₃ = 0.512 * 0.2

    P₃ = 0.1024

    Therefore, the probability that there are exactly 3 customers in the system is 0.1024
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