JOHN CARROLL UNIVERSITY DEPARTMENT OF ECONOMICS AND FINANCE EC 207 BUSINESS STATISTICS PROBLEM SET 2 NAME __________________ PART ONE: MULTIPLE CHOICE. Choose the option that BEST completes the statement or question. (3 points each) 1. Suppose the following are values that represent the variance for a set of data. Which one is obviously incorrect? a. 25 b. 2000 c. 0 d. -14 e. 000037 2. A retailer is considering coding all inventory items with a four digit code using the digits from 0 to 9. How many different codes are possible? a. 30240 b. 210 c. 5040 d.10000 e. supply your own answer ____________ 3. Assume events A and B are independent. The likelihood of event A occurring is 0.70 and of event B occurring is 0.10. Which of the following is TRUE? a. P(A or B) = .6 b. P(A or B) = P(A) + P(B) - P(A and B) = .72 c. P(A and B) = .8 d. P(A or B) = .07 e. P(A and B) = .07 4. When all values in a set of data are equal in value, the variance would equal: a. the mean b. the median c. zero d. it would depend upon whether it was a sample or a population. e. cannot be determined from the above set of information. 5. Which of the following is FALSE concerning a probability tree? a. If probabilities are added for each end point of all branches, the sum is one. b. The tree facilitates analysis of joint probabilities. c. Conditional probability can be reflected in a tree. d. A probability tree may reflect only two possible outcomes. e. The end of a series of branches identifies an intersection event. 6. The probability that an XM missile will hit its target is . Five missiles are fired independently of one another, with the first four missing the target. What is the probability that the fifth missile will successfully hit the target? a. .75 b. .002 c. .24 d. .1875 e. supply your own answer ____________ 7. Which of the following is a TRUE statement? a. The mean is the most commonly occurring value in a group of numbers. b. The value of the median must equal the value of the mode. c. Two different groups of numbers may have arithmetic means which are equal to the same value. d. The mode is the middle value in an ordered array of numbers. e. None of the above statements are true. 8. The following four events are defined to contain certain numbers. A = (1, 3, 5) B = (5, 8, 9) C = (1, 2, 3, 4) D = (7, 9) Which of the following compound (joint) events are mutually exclusive? a. A and B b. A and C c. A and D d. B and D e. None of the above pairs of events are mutually exclusive. 9. The probability that a certain ceramic insulator breaks when first used is 0.10. If it does not break immediately, the probability that it lasts for two years is 0.99. The probability that a new ceramic insulator lasts for two years is: a. 0.891 b. 0.109 c. 0.001 d. 0.099 e. supply your own answer _______________. 10. Events A and B are statistically independent with nonzero probabilities; therefore they must: a. be mutually exclusive. b. have a nonzero intersection. c. have conditional probabilities equal to zero. d. have a union with probability greater than the sum of the probability of A plus the probability of B. e. none of the above. 11. Event A is all months in a calendar year with 30 days or less. Event B includes all twelve months of the year. The union of events A and B includes: a. none of the months b. only those months included in event A. c. only those months not included in event A. d. all twelve months of the year. e. all of the months in the year except February. PART TWO: PROBLEMS. Please do all parts of all problems. Points are allocated as noted and partial credit is possible. 1. A case of twenty cans of food contains one can whose contents are contaminated. Three cans are chosen randomly from this case for testing. a. How many different combinations of three cans could be chosen? (5 pts) b. What is the probability that the can with contaminated contents is among those selected for testing? (6 pts) 2. Of all the students who take the CPA examination, one-fourth have a Master's degree and the remainder have Bachelor's degrees. Half of the students with Bachelor's degrees pass the examination, and three-fourths of those with Master's degrees pass. a. Create a joint probability table that represents this information. (8 pts) b. Find the probability that a student chosen at random from those taking the exam will pass. (5 pts) c. What is the probability that a student both has a Bachelor's degree and passes the examination? (5 pts) d. What is the probability that a student with a Bachelor's degree will not pass the examination? (5 pts) e. What is the probability that a student who has not passed the examination has a Master's degree? (5 pts) f. What is the probability that a student either passes the examination or has a Bachelor's degree, or both? (5 pts) 3. A record store owner believes that the probability that a potential customer entering the store will make a purchase is 0.30. If there are five potential customers in the store, what is the probability that one to four of them will make a purchase? Assume each customer acts independently of the others. (8 pts) 4. Consider the following cumulative frequency distribution: LESS THAN 10 20 30 40 50 CUMULATIVE FREQUENCY 12 36 48 72 84 The smallest number in this data set is 0, the largest is 49. a. Draw the appropriate relative frequency histogram. (10 pts) b. What is the total number of observations used in constructing this distribution? (3 pts) c. What is the absolute frequency of the class \"10 but under 20\"? (4 pts) d. The probability of a randomly selected observation exceeding 20 is: (4 pts) e. The range in this data set is (4 pts) f. What is your point estimate of the sum of the observations used to make this frequency distribution? (5 pts) g. In which class is the median of this data set? (4 pts) h. In which class is the mode? (4 pts) i. Based upon the answers to previous parts of this question, what, if anything, can we say about the skewness of the distribution? (4 pts) 5. Below is the stem-and-leaf display for REVENUE GROWTH rates for the companies generating the fastest revenue growth according to Big Bucks magazine: Stem & Leaf Revenue Growth Leaf Unit = 1.0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 55 01234569 06 0678 05669 016 5 58 0 3 a. For the REVENUE GROWTH rates, identify the 20th percentile. (5 pts) b. What is the mode of REVENUE GROWTH rates? (4 pts) c. Are there any REVENUE GROWTH outliers? If so, what is the value of the outlier? (4 pts) d. Using the REVENUE GROWTH rates, please draw the appropriate box and whiskers display and identify ON THE DIAGRAM the appropriate values of the five number summary. (12 pts) PART THREE. TRUE OR FALSE and explain. For each of the following statements, please answer TRUE or FALSE. If you answer false, please EXPLAIN in one or two sentences why the statement is false. (4 pts each). 1. If events C and D are mutually exclusive, then they are also independent. 2. The sample space for the number of heads in two flips of a coin is S= {0, 1, 2}. Hence the probability of one heads in two flips of a coin is 1/3. 3. A measurement located outside the outer fences of a box-and-whisker display is a quartile. 4. If there are 7 classes in a frequency table then the class containing the median will correspond to the fourth class. 5. The range is a better measure of variation than the standard deviation. 6. An example of a qualitative variable is the mileage of a car