MATH-533 Week 1 Addendum: Homework-Quiz Review – With 100% Correct Answers

MATH-533 Week 1 Addendum: Homework-Quiz Review – With 100% Correct Answers Week 2 Homework and Quiz Review 1. True/False. 2.13 in valid probability. ANSWER: False 2. True/False. The union of two events is the probability of both events occuring. ANSWER: False 3. Determine if each variable below is discrete or continuous: • Number of cars in the parking lot. ANSWER: Discrete • Width of tree trunk. ANSWER: Continuous 4. Given: We have a sample space S with several events defined on it. S={2, 4, 6, 7, 9, 12}. And the events are X={2, 6, 7} and Y={4, 6, 12}. • What is contained in X ∩ Y? ANSWER: {6} • What is contained in X U Y? ANSWER: {2, 4, 6, 7, 12} • What is the complement of Y? ANSWER: {2, 7, 9} 5. Consider the following probability of distribution of number of people we are likely to find waiting in line at a restaurant. Number waiting P(x) 0 .50 1 .30 2 .10 3 .10 • What is the average (mean)? ANSWER: 0.80 • What is the standard deviation? ANSWER: 0.98 • What is P(x=1)? ANSWER: 0.30 • What is P(x>1)? ANSWR: 0.20 6. Consider the following contingency table in which a sample of companies is summarized in terms of the company’s industry type (manufacturing and retail) and country (US, Canada, Mexico). Manufacturin g Retail TOTAL US 10 15 25 Canada 7 4 11 Mexico 6 3 9 TOTAL 23 22 45 • If a company is selected randomly, what is the probability that it is in Canada? ANSWER: P(Canada) = 11/45 = 0.24 • If a company is randomly selected from this group, what is the probability that it is located in Canada and is a retail business? ANSWER: P(Canada ∩ Retail) = 4/45 = 0.09 7. Given: P(D) = .20, P(E) = .13, P(D∩E) = .11. • Find P(D U E). ANSWER: P(D) + P(E) - P(D∩E) = 0.20 + 0.13 - 0.11 = 0.22 • Find P(D’). ANSWER: 1 – P(D) = 1 - 0.20 = 0.80 8. Let N be the event that a person has house in North Dakota, and let F be the event that a person has a house in Florida. It is known that 5% of all people have a house in North Dakota and 12% have a house in Florida. This includes 3% that have a house in both states. NOTE: P(N)=.05 P(F)=.12 P(N∩F)=.03 • Find the probability that among all people, a person has a house in Florida and also in North Dakota. ANSWER: P(N ∩ F) = 0.03 (this is given) • Find probability that person has a house in either North Dakota or Florida or both? ANSWER: P(N U F) = P(N) + P(F) – P(N∩F) = 0.05 + 0.12 – 0.03 = 0.14 9. Assume that 40% of the students who study “hard” get A’s. If the probability that someone studies “hard” is 30%, what is the probability that someone studies “hard” and gets and A. ANSWER: Given - P(A|H) = 0.40, P(H) = 0.30. Find P(H∩A). P(H∩A) = P(H) * P(A|H) = 0.30 * 0.40 = 0.12 10. In a certain binomial distribution problem, n=20 and p=0.10. • What is the average (mean)? ANSWER: 2.00 • What is the standard deviation? ANSWER: 1.34 • Find the probability that x is equal to 3. ANSWER: 0.1901 11. We roll a dice 5 times, what is the probability we will get three 2’s.? ANSWER: Binomial problem. n=5, p=1/6=0.1666667 P(X=3) = 0.0322 12. I participate in 13 races. If the chance of me winning a race is 8%, what is the probability that I win exactly 2 races? ANSWER: Binomial problem. n=13, p= 0.08. P(x=2) = 0.1995 13. A company produces 5000 rulers per day. It is known that 10% of the rulers produced are not accurate. We take a random sample of 50 rulers. (NOTE: n is 50, not 5000) • What is the probability that exactly four rulers are not accurate? ANSWER: Binomial problem. n=50, p=0.10. P(x=4) = 0.1809 • What is the probability fewer than 8 rulers are accurate? ANSWER: P(x<8) = 0.8779 • What is the average (mean)? ANSWER: 5.00 • What is the standard deviation? ANSWER: 2.12 • What is P(X=0)? Answer: 0.0052 14. A recent survey found that 25% of the cars made by Toyota are white. If the probability that a car is made by Toyota is 12.2%, what is the probability that a car is made by Toyota and is white? NOTE: IN GENERAL, when the question asks the probability of one event AND another event, you almost always multiply the two probabilities. Answer: P(W|T)=0.25 P(T)=0.122 P(T∩W) = P(T) * P(W|T) = 0.122 * 0.25 = 0.0305 Show