1. A quiz consists of 15 multiple-choice questions. Each question has five choices, with exactly one correct choice. A student, totally unprepared for the quiz, guesses on each of the 15 questions. How many questions should the student expect to answer correctly?

a.15

b.5

c.3

d.0

2. The annual rainfall in a particular area of the country is normally distributed, with mean 100 cm and standard deviation 20 cm. A drought is said to occur after a year in which the annual rainfall dips below the 20th percentile. For a year to be classified as a year of drought, what would the annual rainfall in this area of the country have to be?

a. 82.3 cm

b. 32.8 cm

c. 23.8 cm

d. 83.2 cm

3. A small community college in Ontario has four student organizations (A, B, C, and D). Organization A has 5 students, B has 8, C has 10, and D has 12. It is thought that new students have no preference for one of these organizations over the other. If seven new students are admitted to the college, what is the probability that one student will choose organization A, one will choose B, two will choose C, and three will choose D?

a. 0.200

b. approximately 0.243

c. approximately 0.059

d. 0.258

4. An eight-cylinder automobile engine has two misfiring spark plugs. The mechanic removes all four plugs from one side of the engine. What is the probability the two misfiring spark plugs are among those removed?

a. 0.2143

b. 0.2314

c. 0.2341

d. 0.2341

5. Given a Poisson random variable x, where the average number of times an event occurs in a certain period of time is 2.5, what is P (x = 0)?

a. 1.5811

b. 0.0821

c. 0.40

d. 2.5

6. A chemical manufacturer sells its product in steel drums. The net weight of the chemical in the drums has a normal distribution with mean 145 kg and standard deviation 2 kg. The manufacturer guarantees its customers each drum will contain at least 140 kg of the chemical. What percentage of the drums will satisfy this guarantee?

a. 98.83%

b. 99.83%

c. 89.83%

d. 99.38%