Question

When things are operating​ properly, a certain Internet bank can process a maximum of 28 electronic transfers every minute during the busiest periods of the day. If it receives more transfer requests than​ this, then the​ bank's computer system will become so overburdened that it will slow to the point that no electronic transfers can be handled. If during the busiest periods of the day requests for electronic transfers arrive at the rate of 180 per​ 10-minute period on​ average, what is the probability that the system will be overwhelmed by​ requests? Assume that the process can be described using a Poisson distribution.

The probability that the system will be overwhelmed by requests is ?

Answer 1

Solution :

Let X ba a random variable which represents the arrivals of electronic transfers.

The arrival rate of electronic transfers = 180 per 10-minute

System will be overwhelmed if it will have more than 28 electronic transfer requests in one minute. And we have to find the probability that the system will be overwhelmed by requests.

It means we have to find P(X > 28) in t = 1 minute

P(X > 28) = 1 - P(X ≤ 28)

P(X > 28) = 1 - [P(X = 0) + P(X = 1)+................+P(X = 28)]

According to poisson process, the probability of occurrence of exactly x events in time t is given by,

Where, λ is rate of occurrence of the event.

We have,  λ = 180 per 10-minute = 18 per minute

t = 1 minute

Using "POISSON.DIST" function of excel we get,

Hence, the probability the system will be overwhelmed by requests is 0.0103.