In examining borrower characteristics versus loan
delinquency, a bank has collected the following information:
(1) 15% of the borrowers who have been employed
at their present job for less than 3 years are behind in
their payments, (2) 5% of the borrowers who have been
employed at their present job for at least 3 years are
behind in their payments, and (3) 80% of the borrowers
have been employed at their present job for at least
3 years. Given this information:
a. What is the probability that a randomly selected
loan account will be for a person in the same job
for at least 3 years who is behind in making
payments?
b. What is the probability that a randomly selected loan
account will be for a person in the same job for less
than 3 years or who is behind in making payments?
c. If a loan account is behind, what is the probability
that the loan is for a person who has been in the
same job for less than 3 years?

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?

4. In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 300 diodes.
(a) How many diodes would you expect to fail on a circuit board, and what is the standard deviation of the number that are expected to fail?
(b) With Poisson distribution approximation, what is the (approximate) probability that at least one diode will fail on a randomly selected board? Round your answer to 2 decimal places.
(c) If ten boards are shipped to a particular customer, how likely is it that at least two of them will work properly? (A board works properly only if all its diodes work)

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?