Question

The probability density function of the time customers arrive at a terminal (in minutes after 8:00 a.m.) is for 0 x. determine the probability that (a) the first customer arrives by 9:00 a.m. (b) the first customer arrives between 8:15 a.m. and 8:30 a.m. (c) two or more customers arrive before 8:40 a.m. among five who arrive at the terminal. assume cus tomer arrivals are independent. (d) determine the cumulative distribution function and use the cumulative distribution function to determine the

Answer 1

The questions relate to the exponential distribution used to model the time between events such as customer arrivals or website visits. The probability of specific time intervals between events is calculated using the exponential distribution formula based on the provided average rates of occurrence.

Step-by-step explanation:

The problems presented involve the concept of an exponential distribution, which is a continuous probability distribution often used to model the time between events in a Poisson process. In this case, the events are customer arrivals, patient visits, website traffic, and airport traffic.

Exponential Distribution and Customer Arrival Times:

For example, if an average of 30 customers arrive at a store per hour, the time between arrivals is exponentially distributed, with an average of 2 minutes between each arrival. To find the probability of a certain time interval for the next arrival, we use the formula for the exponential distribution:

P(X > x) = e-λx, where λ is the rate parameter (number of occurrences per time unit), and X is the random variable representing the time until the next event.