Answer to Question #112323 in Statistics and Probability for Mariamyussifsaeed

Question

At a checkout counter customers arrive at an average of 2 per minute. Find the
probability that
(a) at most 4 will arrive at any given minute.
(b) at least 3 will arrive during an interval of 2 minutes
(c) 5 will arrive in an interval of 3 minutes.

Answer 1

Assume that customers arrival has Poisson distribution with λ=2

Let P_k=the number of arrivals during the given interval.

a) λ=2

P(k≤4)=P₀+P₁+P₂+P₃+P₄= e-^λ(λ⁰/0!+λ¹/1!+λ²/2!+λ³/3!+λ⁴/4!)=0.1429.

b) λ=2*2=4

P(k≥3)=1−P₀​−P₁​−P₂​=1−(4⁰/0!)​⋅e⁻⁴−(4¹/1!)​⋅e⁻⁴-(4²/2!)​⋅e⁻⁴=1-e^-4(1+4+8)=0.7619.

с) Poisson distribution with λ=2*3=6.

P(X=5)=e⁻⁵(λ⁵/5!)​=0.1606.

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