Please show all work and explanation to Receive FULL CREDIT

Please show all work and explanation to Receive FULL CREDIT!!!

Suppose your call center usually gets 30 phone calls per hour. Compute the probability that a phone call will arrive within the next minute.

Solution

Given X~Poisson(mean=30/60=0.5 in a minute)

P(X=x)=(0.5^x)*exp(-0.5)/x!

So the probability is

P(X=1)=(0.5^1)*exp(-0.5)/1 =0.3032653