STAT 201 - EXAM 2 (Practice) Spring 2016 Han Kil Lee Date : Feb. 25, 6:00~6:50 (50 minutes) Place : Davis 209 (Same place as regular lecture) Cover Chapter 5 ~ Chapter 6 Practice exam will be helpful but actual questions will be varied. Formula paper (2-side) Write your name and answers clearly Round all numerical answers to at least nearest 4 decimal places. You need to show step-by-step work as much as possible Circle (or box) your final answer. (If there are multiple answers without a circle/box, you will not be able to get full credit even though one of them is correct answer) Assigned Seating You can use your calculator without the cover (put calculator covers in your bag). Turn off your cell phone; if it is rings or vibrates during the exam, you will get 5 points penalty off of 70. Any electrical device is prohibited (I-pad, I-pod, any mp3 player, etc.) Do not attempt to cheat. Consequences will be severe . Basic Formula (It will not be provided) Probability of Union Probability of A P(A) = Probability of ComP( plement ) = 1 - P(A) Conditional Probability P (A or B) = P(A) + P(B) - P(A and B) P (A|B) = Probability of inter- P (A and B) section = P (A|B)* P (B) = P(B) * P(A|B) Independent events P (A|B) = P (A) P (B|A) = P (B) P (A and B) = P (A) * P (B) Properties of a 1. 0 P(x) 1 probability distribu2. P(x) = 1 tion Expected value = [xP(x)] Binomial probability Z-score Disjoint Events P (A and B) = 0 z= For binomial ranm np and s= = dom variable Empirical Rule for bell shaped data sets Page 0 / 3 STAT 201 - EXAM 2 (Practice) Spring 2016 Han Kil Lee Approximately 68% in of observations fall within 1 standard deviation of the mean Approximately 95% in of observations fall within 2 standard deviations of the mean Approximately 100% in of observations fall within 3 standard deviations of the mean Page 1 / 3 STAT 201 - EXAM 2 (Practice) Spring 2016 Han Kil Lee 1. Suppose a basketball player with two attempts at a free throw has a 60% chance of making his first shot. If he makes the first shot, there is a 70% chance that he will make his second shot. If he misses his first shot, there is a 20% chance the he will make his second shot. Let A = he makes his first shot Let Ac = he misses his first shot Let B = he makes his second shot Let Bc = he misses his second shot B|A A BC|A B|AC AC BC|AC a. Complete the tree diagram by adding 'weights' to the branches. b. What is the probability that he misses both shots? c. What is the probability that he makes first shots given he makes at least one shot? d. What is the probability that he makes at least one shot? 2. Suppose 30 students in a class are asked whether they like a car or bike. Let S = Students in a Class. Let A = students who like car. Let B = students who like bike. N(A)=22, N(B)=18, N(AB)=12 a. If you pick a student, what is the probability that the student likes a car? b. If you pick a student, what is the probability that student does not like a bike? c. How many students do not like both car and bike? d. Are A and B independent events? Verify your answer. e. Are A and B disjoint events? Verify your answer. Page 2 / 3 STAT 201 - EXAM 2 (Practice) Spring 2016 Han Kil Lee Page 3 / 3 STAT 201 - EXAM 2 (Practice) Spring 2016 Han Kil Lee 3. There is a contingency table. X P(X) 0 0.20 1 0.10 2 0.30 3 0.15 4 0.05 5 0.20 1. a. Verify that the probabilities give a legitimate probability distribution b. Compute E(X). 4. When the General social survey most recently asked subjects whether they are a member of an environmental group and whether they would be very willing to pay higher prices to protect the environment, the results were as shown in the table. Pay Higher Price Yes(H) Environmental Group Member No(HC) Yes(M) 30 66 No(MC) 88 933 1. a. What percent of people are willing to pay a higher price, given that they are a environmental group member. b. What is the probability that a person picked randomly is an environmental group member and he is willing to pay a higher price? c. Compute P(H|MC). 5. Assume one has a bell-shaped data set with mean of 40 and standard deviation of 4. a. Find the 90th percentile using the cumulative standard normal distribution table. b. What percentage of data is in the shadowed area? Page 4 / 3 STAT 201 - EXAM 2 (Practice) Spring 2016 Han Kil Lee c. What percentage of data is between 32 and 48? 4. Suppose one has a fair coin and he tosses that coin 100 times. Let X = the number of heads. a. What is the expected value for X? b. What is the variance for X? 5. Suppose one has an unfair coin with 55% to get head, and he toss the coin 5 times. Let X=the number of heads. a. What is the probability that he will get two heads? b. What is the probability that he will get one head? Page 5 / 3