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# exam 1 guide cont MATH 2311

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This 31 page Bundle was uploaded by thanhhakhoagiang@yahoo.com on Monday December 21, 2015. The Bundle belongs to MATH 2311 at University of Houston taught by Leticia Reza in Fall 2015. Since its upload, it has received 1462 views. For similar materials see Intro To Prob & Statistics in Mathematics (M) at University of Houston.

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Date Created: 12/21/15

Math 2311 Written Homework 5 (Sections 4.14.4) Name:__Giang Tran__________________________ PeopleSoft ID:_1372369__________ Instructions: Homework will NOT be accepted through email or in person. Homework must be submitted through CourseWare BEFORE the deadline. Print out this file and complete the problems. Use blue or black ink or a dark pencil. Write your solutions in the space provided. You must show all work for full credit. Submit this assignment at http://www.casa.uh.edu under "Assignments" and choose whw5. 1. Section 4.1, Problem 4 a. b. The probability that X falls below 1.5: P(X<1.5) = 0.5*1/4= 1/8 c. The probability that X lies above 2.5: P(X>2.5) = 1.5*1/4 = 3/8 d. The probability that X lies below 1: P(X<1) = 0 2. Section 4.2, Problem 6 a. The relative frequency of people who take between 49 and 65 minutes to complete the test > pnorm(65,57,8)-pnorm(49,57,8) [1] 0.6826895 b. The interval that contains the middle 95% of completion times for all people taking the test [mean2*sd,mean+2*sd] = [572*8, 57+2*8] = [41,73] 3. Section 4.2, Problem 8 a. The probability that a student in the psychology department has a score less than 480 P (X<480) = > pnorm(480,544,103) [1] 0.2671816 b. The probability that a student in the psychology department has a score between 480 and 730 P(480<X<730) = > pnorm(730,544,103)-pnorm(480,544,103) [1] 0.697345 4. Section 4.3, Problem 8 The value in the set that corresponds to a z-score of 2 is: 2= (x-100)/6 x= 6*2+100 x=112 5. Section 4.3, Problem 12 Only about 5% of young men have heights above the height of: > qnorm(1-.05,68,2.5) [1] 72.11213 (inches) 6. Section 4.3, Problem 15 a. P(Z < 2.15) = pnorm(2.15)= 0.9842224 b. P(2 < Z < 3)= pnorm(3)-pnorm(2)= 0.02140023 c. P(Z > 2) = 1-pnorm(2)= 0.02275013 d. P(−1< Z <1) = pnorm(1)-pnorm(-1)= 0.6826895 e. P(-1.4< Z < 2.01) = pnorm(2.01)-pnorm(-1.4)= 0.8970277 f. P(Z > −1.57) = 1-pnorm(-1.57) = 0.9417924 7. Section 4.3, Problem 20 a. P( X < 230) > pnorm(230,210,32) [1] 0.7340145 b. P(180 < X < 245) > pnorm(245,210,32)-pnorm(180,210,32) [1] 0.688717 c. P( X >190) > 1-pnorm(190,210,32) [1] 0.7340145 d. The value of c such that P( X < c) = 0.0344 > qnorm(0.0344,210,32) [1] 151.7686 e. Find c such that P( X > c) = 0.7486 > qnorm(1-0.7486,210,32) [1] 188.5571 8. Section 4.4, Problem 3 Values of the mean = 40,000 Standard deviation of the sample mean = 3000/sqrt(49) = 428.5714 a. The probability that the average lifetime of the tires sampled was more than 39,500 P(X>39,500)= 1-pnorm(39500,40000,3000/sqrt(49)) = 0.8783275 b. The probability that the average lifetime of the tires sampled was equal to 39,500 P(X=39,500)= 0 c. The probability that the average lifetime of the tires sampled was less than 39,500? P(X>39,500)= pnorm(39500,40000,3000/sqrt(49)) = 0.1216725 9. Section 4.4, Problem 7 a. Values of the mean = 65.4 Standard deviation of the sample mean = 2.8/sqrt(10)= 0.8854377 b. The probability that the sample mean is less than 68 inches > pnorm(68,65.4,2.8/sqrt(10)) [1] 0.9983398 c. The probability that the sample mean is greater than 68 inches. > 1-pnorm(68,65.4,2.8/sqrt(10)) [1] 0.001660226 10. Section 4.4, Problem 10 Values of the mean = 1,637.52 Standard deviation of the sample mean = 623.16/sqrt(400)=31.158 The probability that a simple random sample of 400 accounts has a mean that exceeds $1,650: > pnorm(1650,1637.52,623.16/sqrt(400)) [1] 0.6556203 PRINTABLE VERSION Quiz 1 Question 1 True or False: A sample is a subset of all possible data values for a given subject under consideration. a) False b) True Question 2 True or False: The standard deviation is the square of the variance. a) True b) False Question 3 Which of the following is a measure of variation? a) mean b) standard deviation c) median d) mode Question 4 Which of the following is an example of a data set with 5 values for which the standard deviation is zero. a) 2,2,2,2,2 b) -1,-1,0,1,1 c) 1,2,3,4,5 d) -5,-4,0,3,5 Question 5 If the test scores of a class of 36 students have a mean of 73.1 and the test scores of another class of 28 students have a mean of 67.4, then the mean of the combined group is a) 70.250 b) 70.606 c) 68.106 d) 71.750 Question 6 Given the first type of plot indicated in each pair, which of the second plots could not always be generated from it? a) histogram, dot plot b) stem and leaf, histogram c) stem and leaf, dot plot d) dot plot, histogram Question 7 A survey was conducted to gather ratings of the quality of service at local restaurants. Respondents rated on a scale of 0 (terrible) to 100 (excellent). The data are represented by the following stem plot. The median response was a) 52 b) 50 c) 51.5 d) 51 Question 8 Calculate the mean, median, mode, range and standard deviation of the data: -8, -4, -4, 1, 7 a) mean = -1.6, median = 1, mode = -8, range = 16, standard deviation = 5.8 b) mean = -1.6, median = -4, mode = -4, range = 15, standard deviation = 5.8 c) mean = -0.6, median = -4, mode = -4, range = 15, standard deviation = 5.7 d) mean = -0.6, median = -8, mode = -4, range = 14, standard deviation = 5.7 e) None of the above Question 9 Calculate the mean, median, mode, range and standard deviation of the data: -120, -10, -10, 56, 77 a) mean = -1.4, median = -10, mode = -10, range = 197, standard deviation = 76.9 b) mean = 11.8, median = -120, mode = -10, range = 196, standard deviation = 80.6 c) mean = -1.4, median = 56, mode = -120, range = 198, standard deviation = 76.9 d) mean = 11.8, median = -10, mode = -10, range = 197, standard deviation = 80.6 e) None of the above Question 10 The boxplots shown below summarize two data sets, I and II. Based on the boxplots, which of the following statements about these two data sets CANNOT be justified? a) The median of data set I is equal to the median of data set II. b) The interquartile range of data set I is equal to the interquartile range of data set II. c) The range of data set I is greater than the range of data set II. d) Data set I and data set II have the same number of data points. Question 11 The distribution that has the box plot shown could be described as a) inconclusive b) skewed left c) symmetrical d) skewed right Question 12 The figure below shows a cumulative relative frequency plot of 40 scores on a test given in a Statistics class. Which of the following conclusions can be made from the graph? a) There is greater variability in the lower 20 test scores than in the higher 20 test scores. b) Sixty percent of the students had a test score above 80. c) The median test score is less than 75. d) The horizontal nature of the graph for test scores of 60 and below indicates that those scores occurred most frequently. Question 13 The weights of male and female students in a class are summarized in the following boxplots: Which of the following is NOT correct? a) The male students have less variability than the female students. b) About 50% of the male students have weights between 150 and 185 lbs. c) The mean weight of the female students is about 120 because of symmetry. d) The median weight of the male students is about 166 lbs. Question 14 Given a data set consisting of 33 unique whole number observations, its five-number summary is: How many observations are less than 38? a) 15 b) 17 c) 37 d) 16 PRINTABLE VERSION Quiz 2 You scored 0 out of 100 Question 1 You did not answer the question. A researcher randomly selects 2 fish from among 10 fish in a tank and puts each of the 2 selected fish into different containers. How many ways can this be done? a) 180 b) 90 c) 45 d) 270 e) 40 f) None of the above Question 2 You did not answer the question. An experimenter is randomly sampling 4 objects in order from among 41 objects. What is the total number of samples in the sample space? a) 2430480 b) 101270 c) 9721920 d) 66045 e) 1585080 f) None of the above Question 3 You did not answer the question. A person eating at a cafeteria must choose 4 of the 13 vegetables on offer. Calculate the number of elements in the sample space for this experiment. a) 17160 b) 2860 c) 3024 d) 126 e) 715 f) None of the above Question 4 You did not answer the question. How many license plates can be made using 2 digits and 4 letters if repeated digits and letters are allowed? a) 651006720000 b) 32292000 c) 64584000 d) 45697600 e) 91395200 f) None of the above Question 5 You did not answer the question. The union of two events A and B is the event that: a) Both A and B occur. b) Either A or B or both occur. c) A and B occur at the same time. d) The intersection of A and B does not occur. e) Either A or B, but not both occur. f) None of the above Question 6 You did not answer the question. c Let A = {2, 9}, B = {9, 17, 23}, D = {33} and S = sample space = A ∪ B ∪ D. Identify A . a) {17, 23} b) {17, 23, 33} c) {33} d) {2} e) {2, 17, 23, 33} f) None of the above. Question 7 You did not answer the question. c Let A = {3, 10}, B = {10, 11, 28}, D = {35} and S = sample space = A ∪ B ∪ D. Identify B ∪ A. a) {3, 10} b) {3, 10, 35} c) {3, 11, 28, 35} d) {3, 35} e) {3, 10, 11, 28} f) None of the above. Question 8 You did not answer the question. c c c Let A = {3, 10}, B = {10, 11, 28}, D = {35} and S = sample space = A ∪ B ∪ D. Identify (A ∩ B ) . a) {11} b) {3, 10, 11, 28} c) {3} d) {10} e) {3, 10} f) None of the above. Question 9 You did not answer the question. c Let A = {2, 9}, B = {9, 13, 28}, D = {40} and S = sample space = A ∪ B ∪ D. Identify A ∩ B. a) {9} b) {2, 13, 28} c) {13, 28} d) {9, 13, 28} e) {9, 40} f) None of the above. Question 10 You did not answer the question. In a shipment of 58 vials, only 14 do not have hairline cracks. If you randomly select one vial from the shipment, what is the probability that it has a hairline crack? 22 a) 29 b) 114 7 c) 29 d) 1 58 7 e) 22 f) None of the above Question 11 You did not answer the question. Suppose a card is drawn from a deck of 52 playing cards. What is the probability of drawing a 5 or a king? 1 a) 13 1 b) 156 1 c) ⁄4 d) 213 1 e) ⁄26 f) None of the above Question 12 You did not answer the question. The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.3. The probability that a randomly selected person has high blood pressure and is a runner is 0.2. Find the probability that a randomly selected person either has high blood pressure or is a runner or both. a) 0.8 b) 0.3 c) 0.7 d) 0.5 e) 0.6 f) None of the above. Question 13 You did not answer the question. In a shipment of 58 vials, only 16 do not have hairline cracks. If you randomly select 2 vials from the shipment, what is the probability that none of the 2 vials have hairline cracks? a) 0.5517 b) 0.4483 c) 0.0761 d) 0.0726 e) 0.9274 f) None of the above Question 14 You did not answer the question. The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that a randomly selected person has high blood pressure and is a runner is 0.1. Find the probability that a randomly selected person has high blood pressure and is not a runner. a) 0.4 b) 0.8 c) 0.3 d) 0.6 e) 0.5 f) None of the above. Question 15 You did not answer the question. The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.4 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.5. The probability that a randomly selected person has high blood pressure and is a runner is 0.1. Select the false statement. a) P(R ∪ H ) = 0.9 c b) P(H ∩ R ) = 0.3 c) P(R ∪ H) = 0.8 d) H and R are independent events. e) H and R are not mutually exclusive. f) None of the above. Question 16 You did not answer the question. Hospital records show that 16% of all patients are admitted for heart disease, 26% are admitted for cancer (oncology) treatment, and 8% receive both coronary and oncology care. What is the probability that a randomly selected patient is admitted for coronary care, oncology or both? (Note that heart disease is a coronary care issue.) a) 0.50 b) 0.26 c) 0.58 d) 0.34 e) 0.42 f) None of the above. Question 17 You did not answer the question. Hospital records show that 16% of all patients are admitted for heart disease, 28% are admitted for cancer (oncology) treatment, and 6% receive both coronary and oncology care. What is the probability that a randomly selected patient is admitted for something other than coronary care? (Note that heart disease is a coronary care issue.) a) 0.84 b) 0.78 c) 0.72 d) 0.94 e) 0.66 f) None of the above. Question 18 You did not answer the question. Among 9 electrical components exactly one is known not to function properly. If 2 components are randomly selected, find the probability that all selected components function properly. a) 0.6667 b) 0.7778 c) 0.7023 d) 0.8889 e) 0.2222 f) None of the above Question 19 You did not answer the question. Among 6 electrical components exactly one is known not to function properly. If 4 components are selected randomly, find the probability that exactly one does not function properly. a) 0.6667 b) 0.5000 c) 0.5787 d) 0.8333 e) 0.3333 f) None of the above Question 20 You did not answer the question. Among 8 electrical components exactly one is known not to function properly. If 2 components are randomly selected, find the probability that at least one does not function properly. a) 0.6699 b) 0.1250 c) 0.8750 d) 0.2500 e) 0.7500 f) None of the above PRINTABLE VERSION Quiz 3 Question 1 The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.2 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that a randomly selected person has high blood pressure and is a runner is 0.1. Find the probability that a randomly selected person has high blood pressure, given that he is a runner. a) 0 b) 0.50 c) 1 d) 0.25 e) 0.17 f) None of the above. Question 2 The probability that a randomly selected person has high blood pressure (the event H) is P(H) = 0.3 and the probability that a randomly selected person is a runner (the event R) is P(R) = 0.4. The probability that a randomly selected person has high blood pressure and is a runner is 0.2. Find the probability that a randomly selected person is a runner, given that he has high blood pressure. a) 0.29 b) 0 c) 0.67 d) 0.50 e) 1 f) None of the above. Question 3 The probability that a student correctly answers on the first try (the event A) is P(A) = 0.3. If the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event B). The probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.6. Find the probability that the student correctly answers the question on the first or second try. a) 0.72 b) 0.51 c) 0.90 d) 0.54 e) 0.18 f) None of the above. Question 4 Given the following sampling distribution: X -17 -9 -7 8 16 P(X) 7⁄ 1⁄ 1⁄ 1⁄ ___ 100 50 100 20 What is P(X = 16)? a) 0.83 b) 0.16 c) 0.87 d) 0.85 e) 0.86 f) None of the above Question 5 Given the following sampling distribution: X -16 -11 2 12 20 1 3 9 2 P(X) ⁄20 ⁄100 ⁄100 25 ___ What is P(X > -11)? a) 0.92 b) 0.93 c) 0.89 d) 0.91 e) 0.94 f) None of the above Question 6 Given the following sampling distribution: X -16 -13 -7 11 14 P(X) 225 1 25 2⁄25 7⁄100 ___ What is the mean of this sampling distribution? a) -2.2 b) 8.7 c) 8.4 d) -0.6 e) 8.6 f) None of the above Question 7 Suppose you have a distribution, X, with mean = 29 and standard deviation = 6. Define a new random variable Y = 4X - 5. Find the mean and standard deviation of Y. a) E[Y] = 111; σ Y = 19 b) E[Y] = 116; σ Y = 96 c) E[Y] = 111; σ Y = 96 d) E[Y] = 116; σ Y = 19 e) E[Y] = 111; σ Y = 24 f) None of the above Question 8 In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) at which the missile explodes. The distance X is measured in miles and the sampling distribution of X is given by: X 0 10 50 100 P(X) 1⁄40 120 110 3340 Calculate the mean of this sampling distribution. a) 27.6 b) 86.5 c) 88.0 d) 90.5 e) 761.0 f) None of the above Question 9 In testing a certain kind of missile, target accuracy is measured by the average distance X (from the target) at which the missile explodes. The distance X is measured in miles and the sampling distribution of X is given by: X 0 10 50 100 P(X) 1⁄ 1⁄ 2⁄ 27⁄ 34 17 17 34 Calculate the variance of this sampling distribution. a) 29.4 b) 288.5 c) 4873.6 d) 85.9 e) 865.4 f) None of the above Question 10 Suppose you want to play a carnival game that costs 5 dollars each time you play. If you win, you get $100. The probability of winning is 3 ⁄100. What is the expected value of the amount the carnival stands to gain? a) 2.00 b) 3.00 c) 2.20 d) 2.30 e) -2.00 f) None of the above Question 11 Suppose you want to play a carnival game that costs 5 dollars each time you play. If you win, you get $100. The probability of winning is 3⁄ . What is the expected value of the amount that you, the player, stand to gain? 100 a) -2.00 b) -3.00 c) -2.20 d) -2.30 e) 2.00 f) None of the above Question 12 A random sample of 2 measurements is taken from the following population of values: 0, 1, 3, 4, 7. What is the probability that the range of the sample is 6? a) 0.5 b) 0.2 c) 0.4 d) 0.1 e) 0.3 f) None of the above Question 13 A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers get to the store and that 1 out of 4 buyers change to a more expensive sofa than the one in the sale advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $300 and the more expensive sofa is $450? a) 330.00 b) 337.50 c) 337.72 d) 375.00 e) 412.50 f) None of the above PRINTABLE VERSION Quiz 4 You scored 0 out of 100 Question 1 You did not answer the question. Suppose you have a distribution, X, with mean = 10 and standard deviation = 3. Define a new random variable Y = 5X - 5. Find the mean and standard deviation of Y. a) E[Y] = 50; σY= 10 b) E[Y] = 50; σY= 75 c) E[Y] = 45; σY= 75 d) E[Y] = 45; σY= 15 e) E[Y] = 45; σ = 10 Y f) None of the above Question 2 You did not answer the question. Which statement is not true for a binomial distribution with n = 10 and p = 1/20 ? a) The highest probability occurs wheequals 0.5000 b) The probability thatequals 1 is 0.3151 c) The number of trials is equal to 10 d) The mean equals 0.5000 e) The standard deviation is 0.6892 f) None of the above Question 3 You did not answer the question. In testing a new drug, researchers found that 6% of all patients using it will have a mild side effect. A random sample of 11 patients using the drug is selected. Find the probability that none will have this mild side effect. a) 0.0609 b) 0.5063 c) 0.4937 d) 0.3063 e) 0.9400 f) None of the above Question 4 You did not answer the question. In testing a new drug, researchers found that 3% of all patients using it will have a mild side effect. A random sample of 8 patients using the drug is selected. Find the probability that at least one will have this mild side effect. a) 0.2163 b) 0.9700 c) 0.3378 d) 0.0300 e) 0.1085 f) None of the above Question 5 You did not answer the question. In testing a new drug, researchers found that 3% of all patients using it will have a mild side effect. A random sample of 5 patients using the drug is selected. Find the probability that exactly two will have this mild side effect. a) 0.01821 b) 0.05821 c) 0.03821 d) 0.04821 e) 0.008214 f) None of the above Question 6 You did not answer the question. A manufacturer of matches randomly and independently puts 23 matches in each box of matches produced. The company knows that one-tenth of 8 percent of the matches are flawed. What is the probability that a matchbox will have one or fewer matches with a flaw? a) 0.9855 b) 0.05921 c) 0.9920 d) 0.1542 e) 0.8313 f) None of the above Question 7 You did not answer the question. Suppose you have a binomial distribution with n = 41 and p = 0.4. Find P(8 ≤ X ≤ 12). a) 0.1480 b) 0.0551 c) 0.1551 d) 0.3040 e) 0.1040 f) None of the above Question 8 You did not answer the question. Each year a company selects a number of employees for a management training program. On average, 40 percent of those sent complete the program. Out of the 20 people sent, what is the probability that exactly 9 complete the program? a) 0.3597 b) 0.7553 c) 0.8553 d) 0.1597 e) 0.2037 f) None of the above Question 9 You did not answer the question. Each year a company selects a number of employees for a management training program. On average, 40 percent of those sent complete the program. Out of the 29 people sent, what is the probability that 7 or more complete the program? a) 0.1569 b) 0.0233 c) 0.0569 d) 0.9766 e) 0.9430 f) None of the above Question 10 You did not answer the question. A fish tank in a pet store has 23 fish in it. 8 are orange and 15 are white. Determine the probability that if we select 4 fish from the tank, at least 2 will be white. a) 0.1247 b) 1.1172 c) 0.6521 d) 0.1027 e) 0.8972 f) None of the above Question 11 You did not answer the question. Identify the following distribution as binomial, geometric or neither. A manufacturer produces a large number of toasters. From past experience, the manufacturer knows that approximately 1% are defective. In a quality control procedure, we randomly select 50 toasters for testing. We want to determine the probability that no more than one of these toasters is defective. a) Binomial b) Geometric c) Neither Question 12 You did not answer the question. A quarter back completes 62% of his passes. We want to observe this quarterback during one game to see how many pass attempts he makes before completing one pass. What is the probability that the quarterback throws 4 incomplete passes before he has a completion? a) 0.0129 b) 0.0049 c) 0.9870 d) 0.9950 e) 0.0269 f) None of the above Question 13 You did not answer the question. A quarter back completes 36% of his passes. We want to observe this quarterback during one game to see how many pass attempts he makes before completing one pass. Determine the probability that it takes more than 13 attempts before he completes a pass. a) 0.0010 b) 0.9989 c) 0.9969 d) 0.0030 e) 0.0230 f) None of the above Question 14 You did not answer the question. Joe has an 54% probability of passing his statistics quiz 4 each time he takes it. What is the probability he will take no more than 5 tries to pass it? a) 0.0205 b) 0.0111 c) 0.9888 d) 0.9794 e) 0.0331 f) None of the above Question 15 You did not answer the question. Joe has an 14% probability of passing his statistics quiz 4 each time he takes it. How many times should Joe expect to take his quiz before passing it? a) 10 b) 7 c) 5 d) 21 e) 98 f) None of the above

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