STATS 154 Study Guide for Exam #2
STATS 154 Study Guide for Exam #2 STATS 154
Minnesota State University, Mankato
Popular in Elementary Statistics
Popular in Statistics
This 5 page Study Guide was uploaded by Madison Gottschalk on Friday February 12, 2016. The Study Guide belongs to STATS 154 at Minnesota State University - Mankato taught by Mezbahur Rahman in Fall 2016. Since its upload, it has received 135 views. For similar materials see Elementary Statistics in Statistics at Minnesota State University - Mankato.
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Date Created: 02/12/16
STATS 154 Exam #2 Focus: Chapter 3 Test: Monday, Feb. 15, 2015 1. Make a subjective probability assignment and formalize the basis for your assignment of each of the following: a. At least one of your professors will not show up for class tomorrow. b. A fellow student picked at random will be able to graduate from a high school in your city. c. There will be a major rainstorm or snowstorm three weeks from today. d. You will meet and chat with the president of your country sometime in the next five years. e. A thumbtack when dropped on hardwood floor will land point up 2. A fair coin is thrown in the air five times. If the coin lands with the head up on the first four tosses, what is the probability that the coin will land with the head up on the fifth toss? a. 0 b. 1/16 c. 1/8 d. ½ 3. The probability that the Minnesota River will flood in any given year has been estimated from 100 years of historical data to be 1 in 20. This means: a. The Minnesota River will flood every 20 years b. In the next 100 years, the Minnesota River will flood exactly 5 times. c. In the last 100 years, the Minnesota River flooded exactly 5 times. d. In the next 100 years, it is very likely that the Minnesota River will flood exactly 5 times. 4. Given the P(A) = 1/3, P(B) = ½ and P(A|B) = ½. a. Find P(A ∩ B). b. Find P(B|A). c. Find P(A U B). d. Are A and B independent? Why or why not? e. Are A and B mutually exclusive? Why or why not? 5. Given that P(A ∩ B) = 0.40, P(A|B) = 0.80 and P(A) = 0.60: a. Find P(B) b. Find absolute value of P(A) c. Find P(B|A) d. Find P(A U B) e. Are A and B independent? Why or why not? f. Are A and B mutually exclusive? Why or why not? 6. Toss a fair coin three times. Let A be the event that the second toss is a head and B be the event that there are in total two heads. Answer the following questions: a. Find P(A) b. Find (B) c. Find P(A ∩ B) d. Find P(B|A) e. Find P(A U B) f. Are A and B independent? Why or why not? STATS 154 Exam #2 Focus: Chapter 3 Test: Monday, Feb. 15, 2015 g. Are A and B mutually exclusive? Why or why not? 7. Bob went to buy a new car and has everything picked out except for the body style, color, and radio. If he has four different body styles, eight different colors (he is considering only one color of car) and three different radios, how many different choices does he have to select from? 8. If a die is rolled twice, what is the probability that the first toll yields a 5 or a 6 and the second roll is anything but a 3? 9. In the Big Mac Burger Company there are five economists and seven engineers. A committee of two economists and three engineers is to be formed. In how many ways can this be done if: a. One particular engineer must be on the same committee b. Two particular economists cannot be on the same committee 10. How many different three-member teams can be formed from six students? a. 20 b. 120 c. 216 d. 720 11. From 5 men and 4 women, how many committees can be selected consisting of: a. 3 men and 2 women? b. 5 people of which at least 3 are men? 12. A shipment of 25 computers has arrived at a store. The manufacture of the computers called the store manager saying that seven of the computers were defective. a. If the store has already sold five of these computers, what is the probability that one is defective? b. If the store has already sold five of these computers, what is the probability that none is defective? c. If the store has already sold five of these computers, what is the probability that at most one is defective? 13. An urn contains four white and three red balls. Two balls are drawn. What is the probability that they are the same color if: a. They are drawn without replacement b. The first ball is replaced before the second is chosen (with replacement)? 14. A marble is randomly selected from an urn containing seven red marbles and three blue marbles. A marble is also selected from another urn with two black marbles and three blue marbles. a. What is the probability that both the marbles selected will be blue? b. What is the probability that both will be red? c. What is the probability that one of the marbles will be blue and the other will be red? 15. Jay Nomoth, baseball star, has been at bat 480 times and has made160hits. a. What is the probability that Nomoth will get a hit? b. What is the probability that he will not get a hit? STATS 154 Exam #2 Focus: Chapter 3 Test: Monday, Feb. 15, 2015 16. Use the information concerning 400 individuals in the following table to answer the questions: Checking Account No Checking Account Savings Account 175 50 No Savings Account 100 75 a. What is the probability of selecting an individual who has a checking account? b. What is the probability of selecting an individual who had a savings account? c. What is the probability of selecting an individual who has both a savings account and a checking account? d. Is having a checking account independent of having a savings account? e. What is the probability of selecting an individual who has a checking account, given that the individual has a savings account? 17. You roll two fair dice, a green one and a red one. a. Are the outcomes on the dice independent? b. Find P( 5 on green die and 3 on red die). c. Find P( 3 on green die and 5 on red die) d. Find P( 5 on green die and 3 on red die) or (3 on green die and 5 on red die) e. What is the probability of getting a sum of 6? f. What is the probability of getting a sum of 4? g. What is the probability of getting a sum of 6 or 4? Are these outcomes mutually exclusive? 18. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. a. Are the outcomes on the two cards independent? Why? b. Find P( 3 on the first card and 10 on second). c. Find P(10 on the first card and 3 on second). d. Find the probability of drawing a 10 and a 3 in either order. e. Find the probability that the second card is a club given that the first card is an ace. f. Find the probability that the second card is an ace given that the first card is a club. 19. Based on data from Statistical Abstract of the United States, 112 Edition, only about 14% of senior citizens (65 years old or older) get the flu each year. However, about 24% of the people under the age of 65 years old get the flu each year. Senior citizens (65 years old or older) consist of 12.5% of the general population. a. What is the probability that a person selected at random from the general population is a senior citizen and will get the flu this year? b. What is the probability that a person selected at random from the general population is a person under age 65 and will get the flu this year? 20. Diagnostic tests of medical conditions can have several types of results. The test result can be positive or negative, whether or not a patient has the condition. A positive test (+) indicates that the patient has the condition. A negative test (-) indicates that the patient does not have the condition. Remember, a positive test does not prove that the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some STATS 154 Exam #2 Focus: Chapter 3 Test: Monday, Feb. 15, 2015 who have a medical condition and some who do not. Results of a new diagnostic test for the conditions are shown. Condition Present Condition Absent Row Total Test Result (+) 110 20 130 Test Result (-) 20 50 70 Column Total 130 70 200 Assume the sample is representative of the entire population. For a person selected at random, compute the following probabilities. a. P(+ | condition present); this is known as the sensitivity of a test b. P(- | condition present); this is known as the false-negative rate c. P(- | condition absent); this is known as the specificity of a test d. P(+ | condition absent); this is known as the false-positive rate e. P(condition present and +); this is the predictive value of the test 21. The state medical school has discovered a new test for tuberculosis. (if the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.82, given that a person has tuberculosis. The probability is 0.09 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will a. Have tuberculosis and have a positive test? b. Not have tuberculosis? c. Not have tuberculosis and have a positive test? 22. In a sales effectiveness seminar, a group of sales representative tried two approaches to selling a customers a new automobile; the aggressive approach and the passive. For 1,160 customers, the following record was kept: Sale No Sale Row Total Aggressive 270 310 580 Passive 416 164 580 Column Total 686 474 1160 Suppose a customer is selected at random from the 1,160 participating customers. Let us use the following notation for events: AG = aggressive approach, PA = passive approach, SA = sale and NS = no sale. So, P(AG) is the probability that an aggressive approach was used, and so on. a. Compute P(SA), P(SA|AG) and P(SA|PA) b. Are the events SA and PA independent? Explain. c. Compute P(AG ∩ SA) and P(PA ∩ SA) d. Compute P(NS) and P(NS | AG) e. Are the events NS and AG independent? Explain. STATS 154 Exam #2 Focus: Chapter 3 Test: Monday, Feb. 15, 2015 f. Compute P(AG U SA). 23. Class records of South Central College indicate that a student selected at random has a probability of 0.77 of passing French 101. For the student who passes French 101, the probability that he or she will pass Literature 107 is 0.25. What is the probability that a student selected at random will pass both French 101 and Literature 107? 24. A teacher is making a multiple choice quiz. She wants to give each student the same questions, but have each student’s questions appear in a different order. If there are 10 questions in the quiz, how many different question sets can be formed? 25. A basketball coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters? What is the probability that the five youngest players are the starters? 26. There are ten juniors and twenty seniors in the service Club. The club is to send 5 representatives to the State Conference. a. How many different ways are there to select a group of five students to attend the conference? b. If the members of the club decide to send two juniors and three seniors, how many different groupings are possible? c. If five members are randomly selected, what is the probability that there will be two juniors and three seniors in the group? 27. From a group of 5 men and 7 women, five persons are to be selected to form a committee, what is the probability that at least 3 men are there on the committee? 28. In how many different ways can the letters of the word ‘TAKING’ be arranged in such a way that the vowels always come together? 29. In how many different ways can the letters of the word ‘GUIDING’ be arranged in so that the vowels always come together? 30. Out of 9 consonants and vowels, how many words (not necessarily meaningful) of 3 consonants and 2 vowels can be formed? 31. There are 20 people who work in an office together. Four of these people are selected to go to the same conference together. How many such selections are possible? What is the chance that any specific individual will be included in the trip? 32. Serial numbers for a product are to be made using three letters (using any letter of the alphabet) followed by two single-digit numbers. For example, PQS17 is one such serial number. How many such serial numbers are possible if neither letters nor numbers can be repeated? 33. A 7-card hand is chosen from a standard 52-card deck. How many of these will have four spades and three hearts? What is the chance that if 7-card is selected, there will be four spades and three hearts?
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