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Directions: answer questions 1 – 7 below

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Directions: answer questions 1 – 7 below. Write up your answers in a Word document. Send your Word document and your supporting Excel spreadsheet as attachments to me.
 

Background: Boston Duck Boat Tours LLC has hired you as a Safety consultant. Some time ago,

Baltimore’s inner-harbor water taxi service had one of their water taxis sink due to overloading.

Wanting to avoid the same kind of calamity, Boston Duck Boat has asked you to review their

passenger loading policies.

You have the following information to work with:

1. Each Duck Boat has a seating Capacity of 25 passengers and a maximum passenger load

of 4700 pounds. .

2. According to NIH data, adult body weights are normally distributed with a mean of

172.9 pounds and a standard deviation of 45.8 pounds.

Questions: .

 

1. What is the largest mean weight that 25 adult passengers can have without exceeding the 4700-pound maximum passenger load?

 

2. If a Duck Boat is filled with 25 randomly selected adult passengers, what is the probability that the mean weight of the 25 passengers exceeds the largest mean weight from (1)? (Hint: CLT for sample mean.)

 

3. Compute the probability that the total weight of 25 randomly selected adult passengers exceeds the 4700-pound maximum passenger load. Should this probability agree with the previous probability? Does it agree with the previous probability? (Hint: CLT for sample sums.)

 

4. Suppose the probability that an overloaded boat capsizes is 50%, and that the | probability that a Duckboat that is not overloaded capsizes is .1%. Complete the following tree diagram by filling in the boxes A — H with the missing probabilities (note: you can simply list the values: A= ...,B=..., etc., rather than filling in and submitting the

actual tree diagram).

 

OS BT

Coons Ze O01 = P(not overloaded AND capsizes) = LT

Not a, Does not . }

/ capsize LI = Pout overloaded AND duesu't Cappize} = L— oe 1, .

Oran Capsizen a |] = Plowerloaded AND capsizes) = [4 as s

wT eS

Does no . a

capsize ' ™ “ = Ptoverloaded AND doesn't capsize) = [- oe

5. tf a Duck Boat makes 100 trips with 25 randomly selected adult passengers each trip, should Boston Duck Boat Tours LLC be worried about having a capsize? Why, or why not? Explain, using evidence from your analysis so far.

6. Following the event in Baltimore, the inner-harbor water taxi service decreased the seating capacity in all of its water taxis. Boston Duck Boat Tours LLC is thinking about doing the same thing, i-e., decreasing seating capacity in their Duck Boats to 20. In your opinion as a safety consultant, would this be a good idea? How does this scenario compare to the 25-passenger scenario? Is it safer? Explain.

7. What do you think is an acceptable level of risk? Decreasing the seating capacity would seem to lower the chance of capsizing due to overloading, but it also decreases the revenue (5 fewer seats means 5 fewer tickets sold each trip).

In any “everyday” event, there is a non-zero probability that something catastrophic happens (the elevator you’re in crashes, you’re ina terrible traffic accident driving to

4 the store, etc.). In your personal opinion, where would you draw the line in terms of the probability of a catastrophe occurring in an “everyday” event? On which side of your

o line are Boston Duck Boat Tours’ 20 and 25 passenger seating capacities:

oe a galas