Question

On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour.

a. What is the appropriate probability distribution for X? Explain how X satisfies the

Answer 1

The appropriate probability distribution for the number of cars arriving at the drive-up window of a bank every hour is the Poisson distribution.

Step-by-step explanation:

The appropriate probability distribution for the random variable X, which represents the number of cars arriving at the drive-up window of a bank in any hour, is the Poisson distribution. This distribution is used when the events occur randomly and independently over time, and the average rate of occurrence is known.

The Poisson probability mass function is given by P(X = k) = (e^-λ * λ^k) / k!, where λ is the average number of events occurring in a given time interval. In this case, the average number of cars arriving in an hour is 6.7, so the probability mass function for X would be:

• P(X = 0) = (e^-6.7 * 6.7^0) / 0!
• P(X = 1) = (e^-6.7 * 6.7^1) / 1!
• ...
• P(X = k) = (e^-6.7 * 6.7^k) / k!