Question

A call center in Perth, Australia receives an average of1.3 calls per minute. By looking at the date, a Poissondiscrete distribution is assumed for this variable. Calculateeach of the following

.a. The probability of receiving no calls in the firstminute of its office hours.

b. The probability of receiving 1 call in the first minute.

c. The probability of receiving 3 calls in the first minute.

Answer 1

Solution:

Poisson Formula : Poisson experiment, in which average number of successes within given region is μ. Then, the Poisson probability is:

P(x; μ) = (e-μ) (μx) / x!

where x is the actual number of successes that result from the experiment, and e is approximately equal to 2.71828.

average = μ = 1.3 calls per minute

a)

P( receiving no calls ) = P(x = 0)

=  (e-1.3) (1.30) / 0!

= 0.272532

= 0.2725 (rounded to 4 decimal )

b)

P(receiving 1 call) = P(x=1)

= (e-1.3) (1.31) / 1!

= 0.354291

= 0.3543 (rounded to 4 decimal )

c)

P(receiving 3 calls) = P(x=3)

= (e-1.3) (1.33) / 3!

= 0.099792

= 0.0998 (rounded to 4 decimal )