At the local petting zoo, 65% of the goats are female.  A researcher selects a sample of five of the goats and notes that three are female.  What are p and p^ (p-hat) for female goats?

6. Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the mean and standard deviation of X are 11 gallons and 5 gallons, respectively.
(a) In a sample of 50 randomly selected customers, what is the approximate probability that the sample mean of the amount purchased X is at least 12 gallons? [Hint: use the central limit theorem]
(b) In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at least 600 gallons?

Payoff Table for Bidding and Hosting Sporting Events

                                     Event A                         Event B

Cost of Bidding.           $200,000.                 $10,000

Probability Being Awarded 0.1.                      0.9

Cost of Hosting           $1,000,000.                $60,000

Probability of Hosting

Successfully                0.7                                0 .9

Financial Benefit Expected by an Excellent Event

(including revenue for the convention center and

economic impact for the city)

For event A $50,000,000 and for event B $3,750,000

Financial Benefit Expected by a Mediocre Event

(including revenue for the convention center and

economic impact for the city)

For Event A $38,000,000 for event B$1,600,000

Construct a decision tree as the sport marketing manager of the local sports commission

and convention and visitors bureau (CVB) for Jeffersonville.

Compare the three alternatives (Event A, Event B, or not bidding for any event) for their

expected values and net gains.

Prepare your recommendation to the executives from the sports commission and

convention center and be prepared to explain your decision tree model and the preferred

choice.

Calculate the expected value and the net gain for Event A with the new probability of .3

for being awarded the event, and compare the new outcome for Event A with the

outcome of Event B from previous assignment.

2. What would your recommendation to the executives be now?

3. What are three main take-aways from this exercise?

Ottawa's Confederation Line trains arrive at peak times at a station
to a station on a Poisson basis, averaging 10 trains per hour.
1. What is the waiting time distribution of three trains? What is the
What is the probability that this waiting time is at most 25 minutes? What
What are the mean and variance of this random variable?
2. No train arrives during the first 5 minutes of waiting. What is the
What is the probability that there will be no train during the next 3 minutes?
3. What is the probability that two trains will arrive in twelve minutes?
4. At 95%, at least one train arrives in t-minutes. What is approximately
t in minutes?
5. A period of 5 minutes is said to be empty if it contains no arriving
of trains. What is the probability that at most one 5-minute period
is empty in one hour?