19) If an average of 12 customers are served per hour, what is the probability that the next customer will arrive in 3 minutes or less? Note: λ = 12/60

The probability that the next customer will arrive in 3 minutes or less is; 0.4512

This is a Poisson distribution problem with the formula;

P(X > t) = e^(-λt)

Where;

λ is arrival rate

t is arrival time

We are given;

λ = 12/60

t = 3 minutes

P (X ≤ 3) = 1 - (P(X > 3))

Thus;

P (X ≤ 3) = 1 - e^((12/60) × 3)

P (X ≤ 3) = 1 - 0.5488

P (X ≤ 3) = 0.4512

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The probability that the next customer will arrive in 3 minutes or less is 0.45.

Step-by-step explanation:

Let N (t) be a Poisson process with arrival rate λ. If X is the time of the next arrival then,

Given:

t = 3 minutes

Compute the probability that the next customer will arrive in 3 minutes or less as follows:

P (X ≤ 3) = 1 - P (X > 3)

Thus, the probability that the next customer will arrive in 3 minutes or less is 0.45.