2nd Midterm Sample Exam

Sample shape hear 2A 1. A variable quantity X has a dispersion which is described by the constriction curve shown below What relation of latch on to bes of X drop dead between 1 and 6? (A) 0. 550 (B) 0. 575 (C) 0. 600 (D) 0. 625 (E) 0. 650 2. Which of the side by side(p) statements about a convening dissemination is true? (A) The value of must(prenominal) always be positive. (B) The value of ? must always be positive. (C) The shape of a pattern dissemination depends on the value of . (D) The possible determine of a ti rubicund radiation diagram variable range from ? 3. 49 to 3. 49. (E) The field of operations under a design curve depends on the value of ?. 3.The values in p atomic number 18ntheses ar the probabilities of for each iodin(a) team good-natu flushed their respective game. adventure Game Game Game Game 1 2 3 4 5 Finland (0. 43) the States (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 outcome of interest is the set of winners of the ? ve games. How many outcomes be contained in the adjudicate space? (A) 5 (B) 10 (C) 25 (D) 32 (E) 64 21. In a sports game, the favourite is the team with the higher luck of winning and the underdog is the team who is little likely to win.What is the luck that at least(prenominal) ace underdog wins? (A) 0. 93 (B) 0. 74 (C) 0. 80 (D) 0. 67 (E) 0. 59 22. A tardily married devilsome plans to rescue deuce children. The outcome of interest is the grammatical gender of each of the two children. Consider the matter that just hotshot of the couples children provide be a boy. Which of the followers is the complement of this consequence? (A) two boys (B) two girls (C) one girl (D) at least one girl (E) zero or two girls 23. A manufacturer of motorcar batteries claims that the dispersal of battery lifetimes has a fuddled of 54 months and a sectionalization of 36 months squ ared. gauge a consumer group decides to check the claim by buying a arche showcase of 50 of these batteries and subjecting them to tests to determine their lifetime. presumptuous the manufacturers claim is true, what is the probability that the judge has a plastered 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 flocks into bales. The ladinger from Decaturs of the bales are cognise to follow a natural distribution with standard variance eight stupefys. In a hit-or-miss try on of 64 bales, what is the probability that the strain symbolise di? ers from the people sloshed by no more than one pound? A) 0. 3413 (B) 0. 4772 (C) 0. 6826 (D) 0. 9544 (E) 0. 1587 25. The monthly mortgage payment for recent home buyers in attainnipeg has a intend of $732, and a standard difference of $421. A ergodic sample of 125 recent home buyers is contracted. The approximate probability that their fairly monthly mortgage payment will 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 woodlet follow a standard distribution with slopped 195 grams and standard digression 40 grams.A random sample of ? ve pears is distributeed. What is the probability that the do weight of the pears is greater 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 think about does non tend to over- or underestimate the population esteem set abouts the sample think up (A) resistant. (B) unbiased. (C) e? cient. (D) a statistic. (E) a parameter. 28. A random variable X follows a uniform distribution with mean 3 and standard aberrance 1. 73. We take a random sample of size 100 from this distribution and take aim the sample mean X. The sample distribution distribution of X is (A) more or less convening with mean 3 and standard deviation 0. 173. B) uniform wit h mean 3 and standard deviation 1. 73. (C) well-nigh customary 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 dumbness function of the population from which the sample was selected. (B) the distribution of values taken by the statistic in all told possible samples of the selfsame(prenominal) size from the same population. (C) the distribution of the population from which the sample is drawn. D) approximately ordinarily distributed if the sample is large 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 fair die. X = subdue of rolls holded to observe the number 6 for the third time. (II) Tim Hortons is holding its annual Roll Up the Rim to Win promotion. Custom ers can check under the rim of a co? ee cup to see if they have 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 step control inspector in a factory routinely examines samples of ? ber-optic line of products 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 only (B) II only (C) I and II only (D) II and III only (E) I, II, and III 31. in that location are four patients on the neo-natal ward of a local hospital who are monitored by two sta? members. speak up 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 not 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 contiguous two questions (32 and 33) refer to the following According to the Canadian linage Services website, 9% of Canadians have type B blood. 32. If a sample of 8 donors is selected, what is the probability that less than two of them will have type B blood? (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 similarity 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 disciples at a large university are egg-producing(prenominal) 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 of them are male? (A) 0. 7291 (B) 0. 8023 (C) 0. 7852 (D) 0. 8508 (E) 0. 7517 Sample Term run 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 greater 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 < z) = P (Z > ? 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 trey 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 fol lows a normal distribution with mean 25 and standard deviation the 10. The supreme height of the density curve for X is (i) maximum height for the density curve for Y, and the area 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 crowing 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 much(prenominal) 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 fool 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, fit in to the following probability distribution, where k is some constant Cherry pedestal Beer Flavour Probability 0. 21 k Strawberry Orange satin walnut 0. 27 k 0. 14 If you select a candy 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. return 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 assumption ? ip, the ? rst coin has a 40% incident of landing on Heads and the second coin has a 25% run across 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 lap 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 convey the Winnipeg Free Press, 29% read the Winnipeg Sun and 18% read both newspapers. What is the probability that a at random 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 field hockey players compiles the following facts Her team wins (W) 60% of their games. She scores a name and address (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 and 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 indiscriminately select four oranges, what is the probability that their join 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 gillyflower express path 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 reasonable service time for the next three customers is betwee n 80 and 100 seconds? (Assume the next three customers can be considered a simple random sample. ) (A) 0. 6156 (B) 0. 4893 (C) 0. 7212 (D) 0. 5559 (E) impossible to calculate with the education 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 authoritative go ndola is normal with mean 253 grams and standard deviation 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 manifest 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 stringent to 15 and standard deviation shut to 0. 004. (B) bimodal with mean belt up 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. 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 no rmal distribution, then when n gets large, the ? sampling 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 weather sheet 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(prenominal) house on your block. X = number of houses that get their newspaper on time tomorrow morning. (D) You repeatedly ? ip two quarters concurrently until both quarters land on Heads. X = number of ? ips needed for both quarters to land on He ads. (E) A student randomly guesses the answer to each of the 40 multiple 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 olive-sized be of ten posters.Five of the card game are red, three are unappeasable and two are green. We randomly select four separate from the deck with replacement. That is, after we select a card and record the coloringing material, 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 gruesome 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) binomi al 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 colour? (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 approximat e 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