2nd Midterm Sample Exam

Sample stipulation Test 2A 1. A variant X has a dispersion which is described by the tightfistedness crease shown at a lower place What comparison of cheers of X fall between 1 and 6? (A) 0. 550 (B) 0. 575 (C) 0. 600 (D) 0. 625 (E) 0. 650 2. Which of the hold fasting statements about a pattern dispersion is reliable? (A) The value of must everlastingly be positive. (B) The value of ? must always be positive. (C) The shape of a bonny distribution depends on the value of . (D) The possible determine of a regular frequent shifting trope from ? 3. 49 to 3. 49. (E) The ara under a shape curve depends on the value of ?. 3.The values in p arntheses atomic number 18 the probabilities of each team pleasing their respective game. Game Game Game Game Game 1 2 3 4 5 Finland (0. 43) USA (0. 28) Japan (0. 11) Denmark (0. 33) France (0. 18) vs. vs. vs. vs. vs. Germany (0. 57) Switzerland (0. 72) Canada (0. 89) Sweden (0. 67) Scotland (0. 82) 20. The subject of interest i s the set of winners of the ? ve games. How many outcomes atomic number 18 contained in the precedent lieu? (A) 5 (B) 10 (C) 25 (D) 32 (E) 64 21. In a sports game, the favourite is the team with the higher opportunity of winning and the underdog is the team who is slight likely to win.What is the luck that at to the lowest degree unrivaled underdog wins? (A) 0. 93 (B) 0. 74 (C) 0. 80 (D) 0. 67 (E) 0. 59 22. A recently married duad plans to get down twain children. The outcome of interest is the gender of each of the ii children. Consider the import that exactly one of the couples children leave alone be a boy. Which of the chase is the complement of this event? (A) twain boys (B) ii girls (C) one girl (D) at least one girl (E) zero in or both girls 23. A manufacturer of automobile batteries claims that the distribution of barrage life measure has a basal of 54 months and a variance of 36 months squa cherrydish. hazard a consumer group decides to mark out the c laim by purchasing a savour of 50 of these batteries and subjecting them to tests to determine their lifetime. Assuming the manufacturers claim is square, what is the luck that the exemplar has a hold still for lifetime less than 52 months? (A) 0. 1292 (B) 0. 3707 (C) 0. 0091 (D) 0. 4909 (E) 0. 3483 24. A recycling plant compresses aluminum keisters into bales. The weights of the bales are known to follow a ruler distribution with standard divergency eight pound offs. In a haphazard sample of 64 bales, what is the fortune that the sample look upon di? ers from the universe stringent by no more than one pound? A) 0. 3413 (B) 0. 4772 (C) 0. 6826 (D) 0. 9544 (E) 0. 1587 25. The periodic owe payment for recent home buyers in Winnipeg has a entail of $732, and a standard aberrancy of $421. A stochastic sample of one hundred twenty-five recent home buyers is mete outed. The approximate fortune that their average monthly mortgage payment volition be more than $782 is (A) 0. 9082 (B) 0. 4522 (C) 0. 4082 (D) 0. 0478 (E) 0. 0918 26. Weights of pears in an orchard follow a standard distribution with miserly 195 grams and standard excursus 40 grams.A hit-or-miss sample of ? ve pears is takeed. What is the probability that the thoroughgoing weight of the pears is great than one kilogram (i. . , 1,000 grams)? (A) 0. 2795 (B) 0. 3897 (C) 0. 2451 (D) 0. 3264 (E) 0. 4129 27. The fact that the sample cockeyed does non tend to over- or underestimate the commonwealth reckon limits the sample call back (A) resistant. (B) unbiased. (C) e? cient. (D) a statistic. (E) a parameter. 28. A random variable X follows a invariant distribution with mean 3 and standard disagreement 1. 73. We take a random sample of size 100 from this distribution and consider the sample mean X. The sampling distribution of X is (A) just about normal with mean 3 and standard deviation 0. 173. B) resembling with mean 3 and standard deviation 1. 73. (C) approximately nor mal with mean 3 and standard deviation 0. 0173. (D) uniform with mean 3 and standard deviation 0. 173. (E) approximately normal with mean 3 and standard deviation 1. 73. 29. The sampling distribution of a statistic is (A) the denseness function of the population from which the sample was selected. (B) the distribution of values interpreted by the statistic in all possible samples of the same(p) size from the same population. (C) the distribution of the population from which the sample is drawn. D) approximately normally distributed if the sample is jumbo enough, regardless of the shape of the population from which the sample is drawn.(E) all of the above. 30. Which of the following variables has a binomial distribution? (I) You repeatedly roll a decent die. X = number of rolls needed to observe the number 6 for the third time. (II) Tim Hortons is prop its annual Roll Up the Rim to Win promotion. Customers can yellow journalism under the rim of a co? ee cup to obtain if they ha ve won a prize. You buy one cup of co? ee from Tim Hortons each day for a week. X = number of times you win a prize during the week. III) A quality control inspector in a factory routinely examines samples of ? ber-optic cable being produced to check for defects. The inspector examines a 100-foot length of cable. X = number of defects found on the cable. (A) I precisely (B) II only (C) I and II only (D) II and III only (E) I, II, and III 31. There are four uncomplainings on the neo-natal ward of a local hospital who are monitored by two sta? members. cipher the probability (at any one time) of a patient requiring attention by a sta? member is 0. 3. Assuming the patients behave independently, what is the probability at any one time that there will non be su? cient sta? o attend to all patients who need them? (A) 0. 0756 (B) 0. 1104 (C) 0. 0837 (D) 0. 0463 (E) 0. 2646 The adjoining two questions (32 and 33) refer to the following According to the Canadian Blood Services website , 9% of Canadians have type B rent. 32. If a sample of 8 donors is selected, what is the probability that less than two of them will have type B line of merchandise? (A) 0. 8424 (B) 0. 9711 (C) 0. 3721 (D) 0. 4703 (E) 0. 1576 33. Suppose we select a random sample of 175 blood donors and calculate the proportion p ? of individuals with type B blood. The standard deviation of p is ? (A) 0. 0216 (B) 0. 0358 (C) 0. 0417 (D) 0. 0598 (E) 0. 0647The next two questions (34 and 35) refer to the following It is known that 53% of assimilators at a large university are female and 47% are male. 34. If we take a random sample of 12 students at the university, what is the probability that exactly seven of them are female? (A) 0. 1734 (B) 0. 1834 (C) 0. 1934 (D) 0. 2034 (E) 0. 2134 35. If we take a random sample of 200 students at the university, what is the approximate probability that less than half(prenominal) of them are male? (A) 0. 7291 (B) 0. 8023 (C) 0. 7852 (D) 0. 8508 (E) 0. 7517 Samp le Term Test 2B 1. A random variable X is described by the density curve shown below The probability of P (3 ?X ? 6) is equal to (A) 0. 55 (B) 0. 45 (C) 0. 375 (D) 0. 40 (E) 0. 60 2. A random variable X follows a uniform distribution on the interval from 10 to 15. What proportion of values of X are great than 13. 2? (A) 0. 18 (B) 0. 88 (C) 0. 36 (D) 0. 12 (E) 0. 28 3. Which of the following statements about a normal distribution is true? (A) The mean of a normal distribution must always be greater than zero. (B) For a standard normal distribution, P (Z &lt z) = P (Z &gt ? z) for any value z. (C) The height of a normal density curve must always be equal to one. (D) All values must fall within ternion standard deviations of the mean. E) The standard deviation of a normal distribution must always be greater than one. 4. A variable X follows a normal distribution with mean 10 and standard deviation 5. Another variable Y follows a normal distribution with mean 25 and standard dev iation the 10. The uttermost height of the density curve for X is (i) maximum height for the density curve for Y, and the vault of heaven under the density curve for X is (ii) the area under the density curve for Y. (A) (i) greater than, (ii) less than (B) (i) less than, (ii) greater than (C) (i) equal to, (ii) equal to (D) (i) greater than, (ii) equal to (E) (i) less than, (ii) less than 5.Weights of apples handsome in an orchard are known to follow a normal distribution with mean 160 grams. It is known that approximately 99. 7% of apples have weights between 124 and 196 grams. What is the standard deviation of weights of all apples grown in the orchard? (A) 9 grams (B) 12 grams (C) 18 grams (D) 24 grams (E) 36 grams 6. A variable Z has a standard normal distribution. What is the value b such that P (b ? Z ? 0. 36) = 0. 2470? (A) ? 1. 22 (B) ? 0. 68 (C) ? 0. 27 (D) ? 0. 39 (E) ? 0. 55 The next two questions (7 to 8) refer to the following Percentage grades in a large geography class follow a normal distribution with mean 67. and standard deviation 12. 5. 7. What proportion of students in the class draw percentage grades between 60 and 70? (A) 0. 2650 (B) 0. 2750 (C) 0. 2850 (D) 0. 2950 (E) 0. 3050 8. The professor decides to assign a grade of A+ to the students with the top 8% of the grades, and a grade of A to the next best 12%. What is the minimum percentage a student needs to earn a grade of A? (A) 77 (B) 78 (C) 79 (D) 80 (E) 81 9. The contents of bottles of water follow a normal distribution with mean and standard deviation 4 ml. What proportion of bottles have ? ll volumes within 1 ml of the mean? (A) 0. 1974 (B) 0. 987 (C) 0. 6826 (D) 0. 4013 (E) unable to calculate without the value of 10. A candy company manufactures hard candies in ? ve di? erent ? avours, correspond to the following probability distribution, where k is some constant Cherry ensconce Beer Flavour Probability 0. 21 k Strawberry Orange bilsted 0. 27 k 0. 14 If you select a can dy at random, what is the probability that it will be fruit-? avoured? (A) 0. 48 (B) 0. 67 (C) 0. 68 (D) 0. 72 (E) 0. 86 11. concomitant A has probability of 0. 4 to occur and Event B has a probability of 0. 5 to occur. Their union (A or B) has a probability of 0. 7 to occur.Then (A) A and B are mutually exclusive. (B) A and B are not mutually exclusive. (C) A and B are independent. (D) A and B are dependent. (E) both (B) and (C). 12. You have two unsporting coins. On any inclined ? ip, the ? rst coin has a 40% incur of landing on Heads and the second coin has a 25% endangerment of landing on Heads. If you ? ip both coins, what is the probability that at least one of them lands on Heads? (A) 0. 10 (B) 0. 45 (C) 0. 55 (D) 0. 65 (E) 0. 90 13. A fair six-sided die will be rolled. De? ne A to be the event that an even number is rolled and de? ne B to be the event that a prime number is rolled.Which of the following events is the production of A and B? (A) 2 (B) 2, 3, 5 (C) 2, 3, 4 , 5, 6 (D) 3, 5 (E) 1, 2, 3, 4, 5, 6 14. Suppose it is known that 61% of Winnipeg adults contract the Winnipeg Free Press, 29% read the Winnipeg Sun and 18% read both newspapers. What is the probability that a helter-skelter selected adult in Winnipeg reads only one of the two papers (but not both)? Hint Draw a Venn diagram. (A) 0. 54 (B) 0. 50 (C) 0. 45 (D) 0. 72 (E) 0. 47 The next two questions (15 and 16) refer to the following A ice hockey players compiles the following facts Her team wins (W) 60% of their games. She scores a coating (G) in 30% of her games. She gets a penalty (P) in 40% of her games. In 38% of her games, her team wins and she scores a goal. In 24% of her games, her team wins and she gets a penalty. in 15% of her games, she scores a goal and gets a penalty. 15. In any given game, what is the probability that the player scores a goal or gets a penalty? (A) 0. 85 (B) 0. 55 (C) 0. 70 (D) 0. 65 (E) 0. 58 16. Which of the following statements is true? (A) W a nd G are independent. (B) G and P are mutually exclusive (disjoint). (C) W and P are independent. (D) W and G are mutually exclusive (disjoint). (E) G and P are independent. 7. Weights of oranges sold at a supermarket follow a normal distribution with mean 0. 22 pounds and standard deviation 0. 04 pounds. If you helter-skelter select four oranges, what is the probability that their measure weight is less than 1 pound? (A) 0. 9719 (B) 0. 8508 (C) 0. 9332 (D) 0. 7967 (E) 0. 8340 The next two questions (18 and 19) refer to the following The time X taken by a cashier in a grocery butt in express road follows a normal distribution with mean 90 seconds and standard deviation 20 seconds. 18. What is the ? rst quartile (Q1) of the distribution of X? (A) 73. 8 seconds (B) 85. 0 seconds (C) 69. 4 seconds (D) 81. seconds (E) 76. 6 seconds 19. What is the probability that the average service time for the next three customers is between 80 and 100 seconds? (Assume the next three customers c an be considered a simple random sample. ) (A) 0. 6156 (B) 0. 4893 (C) 0. 7212 (D) 0. 5559 (E) impossible to calculate with the schooling given The next two questions (20 and 21) refer to the following The amount X spent (in $) by customers in the grocery store express lane follow some right-skewed distribution with mean $24 and standard deviation $15. 20. What is the probability that the average amount spent by the next three customers is more than $20? Assume the next three customers can be considered a simple random sample. ) (A) 0. 4619 (B) 0. 6772 (C) 0. 8186 (D) 0. 7673 (E) impossible to calculate with the information given 21. What is the probability that the next 40 customers spend less than $1,000 in total? (Assume the next 40 customers can be considered a simple random sample). (A) 0. 5199 (B) 0. 6064 (C) 0. 6628 (D) 0. 5784 (E) 0. 6331 22.The distribution of weights of chocolate bars produced by a plastered instrument is normal with mean 253 grams and standard deviatio n 3 grams. A sample of ? ve of these chocolate bars is selected. There is only a 2. % chance that the average weight of the sample will be below (A) 250. 37 grams. (B) 254. 10 grams. (C) 252. 63 grams. (D) 251. 54 grams. (E) 249. 82 grams. The next two questions (23 and 24) refer to the following A bimodal probability distribution is one with two clear peaks. A random variable X follows a bimodal distribution with mean 15 and standard deviation 4, as shown below 23. Suppose that you take a random sample of 10,000 observations from the population above and make a histogram. You expect the histogram to be (A) approximately normal with mean rigorous down to 15 and standard deviation slopped to 0. 004. (B) bimodal with mean close to 15 and standard deviation close to 0. 04. (C) approximately normal with mean close to 15 and standard deviation close to 0. 04. (D) bimodal with mean close to 15 and standard deviation close to 4. (E) approximately normal with mean close to 15 and standa rd deviation close to 4. 24. Suppose that you take 10,000 random samples of 10,000 observations from the population above and that for each sample, the mean x is calculated. A histogram of resulting xs ? ? would be(A) approximately normal with mean close to 15 and standard deviation close to 0. 0004. B) bimodal with mean close to 15 and standard deviation close to 0. 04. (C) approximately normal with mean close to 15 and standard deviation close to 0. 04. (D) bimodal with mean close to 15 and standard deviation close to 4. (E) approximately normal with mean close to 15 and standard deviation close to 4. 25. The Central Limit Theorem states that ? (A) when n gets large, the standard deviation of the sample mean X gets closer and v closer to ? / n. (B) regardless of the population distribution of a random variable X, when n gets large, ? the sampling distribution of X is approximately normal. C) if a random variable X follows a normal distribution, then when n gets large, the ? sampli ng distribution of X is exactly normal. ? (D) when n gets large, the sample mean X gets closer and closer to the population mean . ? (E) when n gets large, the sample mean X becomes an unbiased estimator of the population mean . 26. Which of the following variables has a binomial distribution? (A) You roll ? ve fair dice, each with face values of 1 through 6. X = total number of dots facing up on the ? ve dice. (B) An air savourless carrying 100 passengers has two emergency exits, one at the front of the plane and one at the back.The airplane makes an emergency landing. X = number of people who leave the plane through the front exit. (C) A paper boy delivers the newspaper to all house on your block. X = number of houses that get their newspaper on time tomorrow morning. (D) You repeatedly ? ip two quarters at the same time until both quarters land on Heads. X = number of ? ips need for both quarters to land on Heads. (E) A student randomly guesses the answer to each of the 40 mul tiple choice questions on this exam. X = number of multiple choice questions the student gets correct. 27. The probability that a certain machine will produce a defective item is 1/4.If a random sample of six items is taken from the output of this machine, what is the probability that there will be at least ? ve defectives in the sample? (A) 1 4096 (B) 3 4096 (C) 4 4096 (D) 18 4096 (E) 19 4096 28. Event A occurs with probability 0. 12. Event B occurs with probability 0. 88. If A and B are mutually exclusive (disjoint) events, then (A) P(A and B) = 0. 11 (B) P(A and B) = 0. 00 (C) P(A or B) = 1. 00 (D) P(A or B) = 0. 11 (E) both (B) and (C) are correct 29. A random variable X follows a binomial distribution with parameters n and p. If the mean and the variance of X are 3. 6 and 2. 2 respectively, then the values of the parameters n and p are, respectively (A) 6 and 0. 6. (B) 18 and 0. 2. (C) 24 and 0. 15. (D) 12 and 0. 3. (E) 12 and 0. 4. 30. A student driving to university must pass through seven sets of tra? c lights. Suppose it is known that each set of tra? c lights are red 35% of the time and that all lights function independently. What is the probability that the student will have to stop at two or more sets of lights on her to university? (A) 0. 6828 (B) 0. 2985 (C) 0. 4893 (D) 0. 7662 (E) 0. 5997 The next three questions (31 and 33) refer to the following We have a depressed decorate of ten planks.Five of the card game are red, three are grim thistle and two are green. We randomly select four cards from the deck with replacement. That is, after we select a card and record the tinct, we put the card back in the deck and thoroughly shu? e them before we select another card. 31. Let X be the number of blue cards that are selected. The distribution of X is (A) binomial with parameters n = 4 and p = 0. 1. (B) binomial with parameters n = 10 and p = 0. 3. (C) binomial with parameters n = 10 and p = 0. 4. (D) binomial with parameters n = 4 and p = 0. 3. (E) normal with parameters = 1. 2 and ? = 0. 92. 32. Let A be the event that the ? st selected card is the only red card in our four selections. Which of the following events is mutually exclusive (disjoint) from the event A? (A) Second card selected is blue. (B) No green cards are selected. (C) Third selected card is the only green. (D) Same number of red and blue cards are selected. (E) Same number of blue and green cards are selected. 33. What is the probability that the ? rst two selected cards are the same tint? (A) 0. 38 (B) 0. 25 (C) 0. 29 (D) 0. 33 (E) 0. 41 The next two questions (34 and 35) refer to the following Suppose it is known that 8% of males are colour blind. 4. In a random sample of 20 males, what is the probability that exactly 3 of them are colour blind? (A) 0. 1212 (B) 0. 1313 (C) 0. 1414 (D) 0. 1515 (E) 0. 1616 35. In a random sample of 500 males, what is the approximate probability that at least 10% of them are colour blind? (A) 0. 03 (B) 0. 04 (C) 0. 05 ( D) 0. 06 (E) 0. 07 Answers Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Term Test 2A A B A A B B B A B E A E C E B D C B D D C E C C E B B A D B C A A E B Term Test 2B A C B D B C E B A B E C A A B C C E A E C A D C B E E E D D D E A C C