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 4 minutes. The pharmacy has promised to fill all prescriptions in 9 minutes.

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

The potential answers are:

A: 8.21%

B: 4.98%

C: 13.53%

D: 9.07%

E: 10.54%

2. 82% of customers are served in less than what time interval?

The potential answers are:

A: 6.86 minutes.

B: 9.83 minutes.

C: 12.72 minutes.

D: 4.83 minutes.

E: 7.33 minutes.

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

The potential answers are:

A: 3.61%

B: 10.08%

C: 19.54%

D: 16.8%

E: 22.4%

4. What is the probability of arrival of at most 3 customers in 12 minutes.

The potential answers are:

A: 94.73%

B: 67.67%

C: 64.72%

D: 62.88%

E: 91.61%