STAT 200 STAT200 Quiz 3 Answers (Penn State University)

STAT 200 STAT200 Quiz 3 (Penn State University)

1. Decide if the probability described is a subjective (personal) probability or a relative frequency probability: A quarter is flipped 2000 times and results in 500 heads. The 25% (500/2000) chance of heads is a
2. Decide if the probability described is a subjective (personal) probability or a relative frequency probability: A recent college graduate claims he only has a 30% chance of finding a job in the next two months. The chance of 30% is a
3. A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. A student picks a discussion section. The two events W = {the TA is a woman} and J = {the TA is Josh} are
4. A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. A student picks a discussion section. The two events W = {the TA is a woman} and M = {the TA is a man} are
5. Lauren wants to wear something warm when she leaves for class. She reaches into her coat closet without looking and grabs a hanger. Based on what she has in her coat closet, she has a 30% chance of picking a sweater, a 50% chance of picking a coat, and a 20% chance of picking a jacket. What is the probability that she will pick a sweater or a coat?
6. A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. Suppose one study is to be randomly selected from all studies conducted over the past 3 years by this large research firm. What is the probability that this study used randomization?
7. A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. What is the probability that the study used randomization, if we already know that the study was a retrospective observational study?
8. A student doing an internship at a large research firm collected the following data, representing all of the studies the firm had conducted over the past 3 years. Define the events E = {the study was an experiment} and U = {the study used randomization}. Are the events E and U independent?
9. For the following statement, determine if it is true or false. If events A and B are known to be independent and P(A) = 0.2 and P(B) = 0.3, then P(A and B) = 0.5.
10. For the following statement, determine if it is true or false. If events D and E are known to be mutually exclusive, then P(D|E) = 0.
11. A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that neither one of them will be successfully cured?
12. Elizabeth has just put 4 new spark plugs in her car. For each spark plug, the probability that it will fail in the next 50,000 miles is 1/100 (which is 0.01), and is independent from one spark plug to the next. What is the probability that none of the spark plugs will fail in the next 50,000 miles?
13. A pair of dice is rolled. What is the probability of that the sum of the two dice from this roll is two?
14. From our Class Survey, 52% of the students reported having tried marijuana, and 24% of students reported that they had tried marijuana and still smoke marijuana. What is the probability that a student still smokes marijuana given that the student has tried marijuana?
15. A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. Two students, Bill and Tom, who don’t know each other, each pick a discussion section. The two events B = {Bill’s TA is Lauren} and T = {Tom’s TA is a woman} are