Question

Describe the seven characteristics (equations) for the following example: Piada Italian Street Food in the Mall of America has an arrival rate of .91 customers per minute and a service rate of 1.19 customers per minute. On the last characteristic, what is the probability that exactly 3, 5, and 10 customers are in the system. Round to five decimals on g-the seventh formulae, and round to 3 decimals on all others. Make sure and label your answers

Answer 1

The characteristics (equations) for the given example include the arrival rate, service rate, average time between two successive arrivals, probability of waiting less than one minute for the next customer, probability of waiting more than five minutes for the next customer, and probabilities of having 3, 5, and 10 customers in the system.

Step-by-step explanation:

The characteristics (equations) for the given example are:

1. The arrival rate is 0.91 customers per minute.
2. The service rate is 1.19 customers per minute.
3. The average time between two successive arrivals is 2.10 minutes. (Reciprocal of the arrival rate)
4. It takes, on average, 6.05 minutes for three customers to arrive. (Dividing the average time between arrivals by the number of customers)
5. The probability that it takes less than one minute for the next customer to arrive is 0.397. (Calculated using the exponential distribution)
6. The probability that it takes more than five minutes for the next customer to arrive is 0.125. (Also calculated using the exponential distribution)
7. The probability that exactly 3 customers are in the system is 0.09109, the probability that exactly 5 customers are in the system is 0.15363, and the probability that exactly 10 customers are in the system is 0.03248. (Calculated using the probability mass function of the Poisson distribution)