Discuss the below:
Q1: In a certain state, an appeals court consists of seven judges. For a routine case, three judges are chosen at random as a panel to hear a case and render a decision. How many distinct panels can be formed?
Q2: Logging trucks have a particular problem with tire failures due to blowouts, cuts, and large punctures; these trucks are driven fast over very rough, temporary roads. Assume that such failures occur according to a Poisson distribution at a mean rate of 4.0 per 10,000 miles.
a. If a truck drives 1000 miles in a given week, what is the probability that it does not have any tire failures?
b. What is the probability that it has at least two failures?
c. What is the expected value and standard deviation of the number of tire failures per 1000 miles driven?
Q3: A financial analyst states that the (subjective probability) price of Y of a long-term $1000 government bond one year later is normally distributed with expected value $980 and a standard deviation $40.
a. Find P(Y ≥ 1000)
b. Find P(Y ≤ 940).
c. Find P(960 ≤ Y ≤ 1060)