Answer:
The value is [tex]P(X = 3) = 0.1798[/tex]
Step-by-step explanation:
From the question we are told that
The rate is [tex]\lambda = 8.6 \ hr ^{-1}[/tex]
General probability distribution for Poisson distribution is mathematically represented
[tex]P(X = x) = \frac{(\lambda * t)^{x} }{x!} * e^{-\lambda * t}[/tex]
Given that is in per hour then the unit of t is in hours
Generally 30 minutes = [tex]0.5 \ hours[/tex]
Generally the probability that 3 customers arrive in the first 30 minutes is mathematically represented
[tex]P(X = 3) = \frac{( 8.6 * 0.5 )^{3} }{3!} * e^{-8.6 * 0.5 }[/tex]
=> [tex]P(X = 3) = 0.1798[/tex]
