its all relatively one question would someone please help me with the answers

1. (5 points) UP Fitness will install 4 new trapezoidal gel-resistance toners, or "trappies," which are the latest exercise gadget specifically designed to contour upper back muscles. Clients who want to use these machines arrive at the rate of 80 per hour. The coefficient of variation of the interarrival times is 2. If all four machines are busy, UP Fitness clients use other pieces of equipment, waiting for one of the "trappies" to become available. The trappy experience is intense120 seconds of explosive exercise intensity. The standard deviation of the usage times (measured in seconds) is quite smallonly 30.

a. On average, how many UP Fitness clients are using a trappy?

b. On average, how many UP Fitness clients are waiting to use a trappy?

2. (5 points) 3) Max Stamp approves study abroad documents for Penn. Students must wait in line with their forms outside Max's office. One student at a time is allowed in his office, and Max takes precisely 25 minutes to evaluate each student's set of documents. On average, 2.2 students per hour go to his office, and they spend on average 160 minutes trying to get their forms approved (time waiting in queue plus time in Max's office for him to evaluate their documents). On average, how many students are waiting outside of Max's office? (Note: Ignore start-of-the-day and end-of-the-day effects.)

3. (5 points) Find a Doctor, or FaD, is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc.). During a "slow" time for them, they have 7 staff members taking calls from customers. On average, one call arrives every

6 minutes (with a standard deviation of 6). Each staff member spends 20 minutes with each customer (on average, with a standard deviation of 10).

a. What is the probability that one of their staff members is busy (as a %)?

b. How long (in minutes) does a customer spend on average waiting on hold before they can start speaking to a representative from FaD?

4. (5 points) The organizers of a conference in the Philadelphia Convention Center are evaluating the possibility of setting up a computer area where attendees can check their e-mail on computers provided by the organization. There will be one common queue for all computers, and only one person uses a computer at a time. On average, there are 15 attendee arrivals per hour, the standard deviation of the time between arrivals is 4, and the average time a person spends on the computer is 10 minutes (with a standard deviation

3). To ensure that waiting times are not too long, the organizers want to ensure that the utilization of the computers doesn't exceed 90%. At least how many computers do they need to have?

5. A city in South Florida is tracking traffic accident data during its peak season for tourism. View the chart below to see these dismal numbers.

Week Traffic Accidents

1 19

2 14

3 27

4 20

5 29

6 31

7 21

8 26

9 28

a. Based on the traffic accident data, how many traffic accidents are forecasted for week 10 using the nave method?

b. Based on the table provided, what is the three-week moving average forecast for week 10?

c. Based on the table provided, what is the four-week moving average forecast for week 11?

d. Assume a smoothing parameter of 0.1 and a forecasted amount of accidents for week 9 was 24. What is the exponential smoothing forecast for week 10?