# The Number of Complaints Which a Bank Manager Receives per Day is a Poisson Random Variable with Parameter M = 4. Find the Probability that the Manager Will Receive - Mathematics and Statistics

Sum

The number of complaints which a bank manager receives per day is a Poisson random variable with parameter m = 4. Find the probability that the manager will receive -

(a) only two complaints on any given day.

(b) at most two complaints on any given day

[Use e-4 =0.0183]

#### Solution

P(X=k)=e^(-m) xx m^k/(k!)

(a) only two complaints on any given day.

k=2, m=4

P(X=2)=e^(-4) xx 4^2/2

=0.0183 xx 8

=0.1464
Probability that the manager will recieve only two complaints on any given day = 0.1464

(b) at most two complaints on any given day

=P(x<=2)

=P(x=0)+P(x=1)+P(x=2)

= e^(-4) + 4e^(-4) + 4^2   (e^(-4))/(2!)

= e^(-4) ( 1 + 4 + 8)

= 13 x e^(-4)

= 13 x 0.0183

= 0.2379

Probab ility that the manager will receive · at most two complaints on any given day = 0.2379.

Concept: Poisson Distribution
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2014-2015 (March)

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