Question 5 Consider the diameters of cylindrical parts manufactured on a computer-controlled lathe.
a) Suppose that the mean of the diameters is known to be 0.1 millimetres. Give an upper bound to the probability that the diameter of new part will exceed 0.11 mm.
b) Suppose that the mean is unknown but the standard deviation is known to equal 0.002 mm. What can be said about the probability that the diameter of a new part will be within 0.006 mm of the unknown mean for that run?
c) How many new parts should be made so as to ensure, with probability at least 0.75, that the average diameter would be within 0.001 mm of the unknown mean? Assume each part is made independently.

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.)

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?