Math 3342-001 Exam I July 14, 2006Answer the problems on separate paper. You do not need to rewrite the problem statements on your answer sheets. Do your ownwork. Show all relevant steps which lead to your solutions. Attach this question sheet to the front of your answer sheets.1. (24 pts) The following are 20 measurements on the strength (pounds) of paper to be used in cardboard tubes:43 78 37 40 68 72 55 62 22 8278 60 50 66 47 56 29 67 83 55Find the following (if they exist) for the above measurements:a. mean b. median c. moded. variance e. Q1f. Q3g. interquartile range h. max i. minj. rangeConstruct the following for the above measurements:k. dot diagram l. modified box-whisker plot2. In a 2-week study of productivity of workers, the following data were obtained on the total number of acceptable pieceswhich 40 workers produced:55 46 39 74 69 65 38 33 57 4653 68 47 30 58 82 65 52 26 7265 36 49 84 79 56 28 43 67 3649 58 66 84 60 61 50 65 66 35a. (12 pts) Construct a frequency distribution (conforming to the guidelines in the text) for the data. Clearlyidentify the following: classes, class marks and class frequencies.b. (4 pts) Construct a histogram to graphically represent the data in the frequency distribution.c. (3 pts) Construct the mean of grouped data in the frequency distribution.d. (5 pts) Construct the variance of the grouped data in the frequency distribution.3. (8 pts) A carton of 22 rechargeable batteries contains six batteries which are defective. a. In how many ways can an inspector select a sample of five batteries and get (exactly) two of the defectivebatteries?b. What is the probability that an inspector who selects a sample of five batteries will get (exactly) three of thedefective batteries?4. (4 pts) The probability that the statistics group (in the math department) will be recognized on campus for researchcontributions to the Tech is 0.18 and the probability that they will be recognized by the American Statistical Association(ASA) for professional contributions is 0.24. The probability that they will receive both awards is 0.12. What is theprobability that they will receive (exactly) one of the two awards?5. (12 pts) To provide prizes for the conclusion for the annual girl scout cookie drive, the local girl scout council haspledged to provide a bag containing two money envelopes (each containing $100), four movie ticket envelopes (eachcontaining tickets for a family of four to go to Movies Sixteen) and two food coupon envelopes (each containingcoupons for a family of four to go to McDonalds) and the national girl scout council has pledged to provide a bagcontaining three money envelopes, two movie ticket envelopes and four food coupon envelopes. At the awardsceremonies for the cookie drive, one of the bags (from one of the councils – the local or the national) will be selected. There is a 75% likelihood that the local council’s bag will be selected and a 25% likelihood that the national council’sbag will be selected. The winning scout will get to randomly select an envelope out of the selected council’s bag. a. What is the likelihood that the randomly selected envelope will be a money envelope?b. What is the likelihood that the randomly selected envelope will be a food envelope?6. (18 pts) Consider the contingency table for passenger cars, SUVs and light trucks in use given below, as reported by theMotor Vehicle Manufacturers Association in Motor Vehicle Facts and Figures. Frequencies are in millions.Age (years)TypeUnder 3(A1)3-5 (A2)6-8 (A3)9-11(A4)12 & over(A5)TotalCar (V1)21.5 29.9 22.2 17.9 15.5 107SUV(V2)10.5 14.1 16.8 8.4 10.2 60Truck (V3)3.2 2.5 2.0 1.8 3.5 13Total35.2 46.5 41 28.1 29.2 180Let E1 be the event that a selected vehicle belongs to either A2 or A3.Let E2 be the event that a selected vehicle belongs to either V1 or V3.Let E3 be the event that a selected vehicle belongs to either A2 or V2.a. Find P(A4)b. Find P(V3)c. Find P(A2 E2 )∩d. Find P(E1 | V2)e. Find P(E1 | E2)f. Find P(E1 E3)∩7. (12 pts) For the above contingency table a digest shows (from repair records) the following probabilities that a SUV willhave had a transmission replacement.Age (years)Under 3(A1)3-5 (A2)6-8 (A3)9-11(A4)12 & over(A5)TotalSUV(V2)10.5 14.1 16.8 8.4 10.2 60Prob. ofTrans.Repl.0.06 0.13 0.25 0.59 0.68a. If a SUV in use is randomly selected, what is the probability that it will have had a transmission replacement?b. If a selected SUV has had a transmission replacement, what is the probability that the selected SUV came fromage group