What is average number of students waiting in line outside

Question

1.A small, family-owned coffee shop does a brisk business every weekday morning. Customers arrive at an average rate of 16 per hour. There is only one server and she can serve a customer in an average of 3 minutes. What is the probability that there are at least 5 customers at the coffee shop?

• 0.95
• 0.80
• 0.75
• 0.59
• 0.00

2.A small, family-owned coffee shop does a brisk business every weekday morning. Customers arrive at an average rate of 16 per hour. There is only one server and she can serve a customer in an average of 3 minutes. What is the probability that the server is not busy?

• 0.00
• 0.80
• 0.75
• 0.20
• 1.00

3.A tutor is working diligently in the tutoring lab answering questions from students the day the homework assignment is due. Because so many students have waited until the last minute to do their homework, she keeps socialization to a minimum and provides explanations as quickly as possible. On average, she can answer 20 questions per hour and students arrive at her office seeking help every four minutes. Student arrivals are Poisson distributed and answer times are exponentially distributed. What is the Utilization rate for the tutoring lab?

• 0.00
• 0.80
• 0.75
• 0.20
• 1.00

4.A decision maker's worst option has an expected value of $1,000, and her best option has an expected value of $3,000. With perfect information, the expected value would be $5,000. The decision maker has discovered a firm that will, for a fee of $1,000, make her position-risk free. How much better off will her firm be if she takes this firm up on its offer?

• $5,000
• $4,000
• $3,000
• $2,000
• $1,000

5.A tutor is working diligently in the tutoring lab answering questions from students the day the homework assignment is due. Because so many students have waited until the last minute to do their homework, she keeps socialization to a minimum and provides explanations as quickly as possible. On average, she can answer 20 questions per hour and students arrive at her office seeking help every four minutes. Student arrivals are Poisson distributed and answer times are exponentially distributed. What is the average number of students waiting in line outside the tutoring lab if each student asks one question?

• 2.25
• 2.80
• 1.75
• 3.20
• 1.00