It is estimated that 040 of the callers to the Customer Serv

It is estimated that 0.40% of the callers to the Customer Service department of Dell Inc. will receive a busy signal.

What is the probability that of today\'s 1,301 callers at least 5 received a busy signal? Use the poisson approximation to the binomial.

Solution

Given X follows Poisson distribution with mean=n*p=1301*0.004=5.204

P(X=x)=(5.204^x)*exp(-5.204)/x!

So the probability is

P(X>=5)=1-P(X=0)-P(X=1)-...-P(X=4)

=1-(5.204^0)*exp(-5.204)/1-...-(5.204^4)*exp(-5.204)/4!

=0.5945439