MATH200 — Practice Quiz: Chapter 6 — 20 min

# Practice Quiz: Chapter 6

Work this like a regular quiz, using only your crib sheet. Give yourself a maximum of 20 minutes, then turn to the solutions and see how you did.

Beware of off-by-one errors! Round probabilities to four decimal places.

Remember, you must show your work for full credit on any problems involving computation.

1(points: 2½)  Suppose 80% of students who register for Elizabethan Sonnets complete the course successfully. And suppose you took many, many samples of six people, with replacement. What would be the expected mean and standard deviation of the number of people that would finish successfully, per sample of six?

A coin is weighted — the chance of heads is not 50%. On five flips of that coin, the probability of various numbers of heads is shown by this probability distribution:
 x P(x) 0 1 2 3 4 5 0.0778 0.2591 0.3456 0.2305 0.0768 0.0102
2(points: 1) What type of probability distribution is this? Answer continuous, discrete, binomial, or categorical.

3(points: 2½) Find the mean and standard deviation of the above probability distribution, and label them with their correct symbols.

4(points: 2)  Long experience shows that a particular drug will help 40% of the people who take it. If you take a random sample of five people, what is the probability that the drug helps at least three?

5(points: 1)  You roll five dice and count the number of twos that appear. List the possible values of the discrete random variable, X = “number of twos in five dice”.

6(points: 2)  Suppose 55% of the people in the area are smokers. If you take a random sample of four people, what is the probability that less than two of them are smokers?

7(points: 4)  A lottery has a 1 in 10 million chance of paying \$10,000,000, a 1 in 125 chance of paying \$100, and a 1 in 20 chance of paying \$10. A ticket costs \$5, and you do not get that money back if you win a prize.
(a) Construct a discrete probability distribution.
(b) Is this a good deal or a bad deal for you? Explain.

Solutions to this practice quiz are available at http://www.tc3.edu/instruct/sbrown/stat/