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?

Question 10 The weekly demand for a product approximately has a normal distribution with mean 1,000 and standard deviation 200. The current on hand inventory is 2,200 and no deliveries will be occurring in the next two weeks. Assuming that the demands in different weeks are independent,
a) What is the probability that the demand in each of the next 2 weeks is less than 1,100?
b) What is the probability that the total of the demands in the next 2 weeks exceeds 2,200?

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?

Question 7 Suppose that 5 independent trials, each of which results in any of the outcomes 0, 1, or 2, with respective probabilities 0.3, 0.5, and 0.2, are performed. Find the probability that both outcome 1 and outcome 2 occur at least once. (Hint: Consider the complementary probability.)