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# The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives at most two complaints on a given d - Mathematics and Statistics

Sum

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives at most two complaints on a given day. Use e−4 = 0.0183.

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#### Solution

Let X denote the number of complaints which a bank manager receives per day.
Given, m = 4 and e–4 = 0.0183
∴ X ∼ P(m) = X ∼ p(4)
The p.m.f. of X is given by

P(X = x) = ("e"^-"m" "m"^x)/(x!)

∴ P(X = x) ("e"^-4(4)^x)/(x!), x = 0, 1, 2,...

P(at most two complaints)
= P(X ≤ 2)
= P(X = 0 or X = 1 or X = 2)
= P(X = 0) + P(X = 1) + P(X = 2)

= ("e"^-4 (4)^2)/(2!) + ("e"^-4 (4)^1)/(1!) + 0.1464   ...[From (i)]

= 0.0183 + 4 x 0.0183 + 0.1464
= 0.2379

Concept: Poisson Distribution
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.4 | Q 1.04 | Page 152
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