dolution

In a single phase single server service process where both interarrival time and service times are exponentially distributed, it can be assumed that the total time that a customer spends in the process is also exponentially distributed. Suppose the total time the customers spend in a pharmacy is exponentially distributed with mean of 6 minutes. The pharmacy has promised to fill all prescriptions in 17 minutes.

1. What percentage of the customers cannot be served within this time limit?

The potential answers are:

A: 11.08%

B: 10.54%

C: 5.88%

D: 6.95%

E: 9.7%

2. 88% of customers are served in less than what time interval?

The potential answers are:

A: 4.83 minutes.

B: 7.33 minutes.

C: 12.72 minutes.

D: 6.64 minutes.

E: 5.14 minutes.

3. What is the probability of arrival of exactly 2 customers in 12 minutes.

The potential answers are:

A: 19.54%

B: 27.07%

C: 18.04%

D: 15.63%

E: 22.4%

4. What is the probability of arrival of at most 2 customers in 12 minutes.

The potential answers are:

A: 91.61%

B: 43.35%

C: 81.53%

D: 67.67%

E: 78.51%