Question

Customers arrat a service window according to a poisson process with an average of 0.2 per minute.

A) What is the probability that the time between two successive arrivals is less than 6 minutes?
B) What is the probability that there will be exactly three arrivals during a given 10-minute period?

Answer 1

The probability that the time between two successive arrivals is less than 6 minutes is approximately 59.3%.

Step-by-step explanation:

To find the probability that the time between two successive arrivals is less than 6 minutes, we can use the exponential distribution formula. The average rate of arrivals is 0.2 per minute, which means that the average time between arrivals is 1/0.2 = 5 minutes. Using the exponential distribution formula, we can calculate the probability of the time between arrivals being less than 6 minutes.

P(Arrival Time < 6 minutes) = 1 - e^(-0.2 * 6) ≈ 0.593

Therefore, the probability that the time between two successive arrivals is less than 6 minutes is approximately 0.593, or 59.3%.

Answer 2

Step-by-step explanation:

Given that customers arrat a service window according to a poisson process with an average of 0.2 per minute

= 12 per hour.

a) the probability that the time between two successive arrivals is less than 6 minutes

= For one hour more than 60/6 =10 customers arrive.

P(X>10) = 0.6528

b) Prob that there will be exactly three arrivals during a given 10-minute period

P(x=3) for average 2

= 0.1804