3 Arrivals at a records and registration teller are exponent

3. Arrivals at a records and registration teller are exponentially distributed at the rate of 30 arrivals per hour. Organize your answers in minutes for this problem. 3.1) What is the probability of zero arrivals in the next minute? 3.2) What is the probability of zero arrivals in the next two minutes? 3.3) What is the probability of two arrivals in the next two minutes?

Solution

a) 30 per hour therefore 30/60 arrivals in 1 minute

probability of zero arrival in next minute = p(x>1) = e^-(1/2*1)=0.60

b) probability (x>2) = e^-(1/2*2)=0.367

c) probability of two in two minutes = 1-e^-(1/2*2) =0.633