Fall 205 Math 4:505 Exam 3 Form A Last Name: First Name: Exam Seat #: UIN: On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work Signature: INSTRUCTIONS Part : Multiple Choice (Problems -8) Each multiple choice problem is worth 6 points for a total of 48 points Answers should be written in the boxes provided No partial credit will be given Part 2: Work Out (Problems 9-3) The number of points for each problem is indicated next to the problem for a total of points Partial credit will be given All steps must be written clearly and neatly to receive credit If you use your calculator for anything beyond an arithmetic calculation, please indicate how at the appropriate step Box your final answer An Aggie does not lie, cheat or steal or tolerate those who do
Part : Multiple-Choice Each multiple choice problem is worth 6 points for a total of 48 points No partial credit will be given Answers should be written in the boxes provided An experiment consists of selecting a card at random from a deck of cards What is the probability that a heart or an ace is drawn? (a) 7 (b) 6 (c) 8 (d) b 2 If E and F are independent events, P(E) = 45, and P(F) = 5, what is P(E c F c )? (a) 775 (b) 725 (c) 275 (d) 225 a 3 Which of the following is an infinite discrete random variable? (a) The number of heads that occur when a coin is tossed five times (b) The distance (in miles) a commuter travels to work (c) The number of boys in a two-child family (d) The number of times a die is rolled until a 6 falls uppermost d 4 If the odds in favor of a team winning a particular football match are 7 to 5, what is the probability that the team will win the match? (a) 5 2 (b) 5 7 (c) 7 2 (d) 7 5 c 2
5 Two light bulbs are selected at random from a lot of 0, of which 4 are defective What is the probability that both light bulbs are defective? (Answers below are rounded to two decimal places) (a) 03 (b) 3 (c) 6 (d) 2 b 6 The personnel department of a company compiled the following data regarding the income and education of its employees: Income $65,000 or below Income above $65,000 Noncollege graduate 2040 840 College graduate 400 What is the probability that a randomly chosen employee has income above $65,000 if it is known that he or she has a college degree? (a) (b) 560 (c) 560 (d) 20 7 Refer to the table in the previous problem What is the probability that a randomly chosen employee has income above $65,000 or is a college graduate? (a) (b) 240 (c) 960 (d) 360 8 A mathematics test consists of eight multiple-choice questions If each question has four possible answers, of which only one is correct, what is the probability that a student who guesses at random on each question will answer at most two questions correctly? (Answers below are rounded to two decimal places) d c (a) 3 (b) 37 (c) 59 (d) 68 d 3
Part 2: Work Out The number of points for each problem is indicated next to the problem Partial credit will be given All steps must be written clearly and neatly to receive credit If you use your calculator for anything beyond an arithmetic calculation, please indicate how at the appropriate step Box your final answer 9 (8pts) Let S = {s,s 2,s 3,s 4,s 5,s 6 } be the sample space associated with an experiment having the following probability distribution: Outcome s s 2 s 3 s 4 s 5 s 6 Probability 2 a 2 b 3 2 (a) Find P({s,s 3,s 5 }) P({s,s 3,s 5 }) = P(s ) + P(s 3 ) + P(s 5 ) = 2 + 2 + 3 = 2 (b) If P({s 3,s 4,s 5 }) = 2 7, find a and b 7 2 = P({s 3,s 4,s 5 }) = P(s 3 ) + P(s 4 ) + P(s 5 ) = 2 + b + 3 = 2 5 + b so b = 2 7 2 5 = 2 2 = 6 All the probabilities should sum to, so a = 2 2 b 3 2 = 2 3 = 4 4
0 (0pts) The relative humidity, in percent, in the morning for the months of January through December in Boston follows: Find the,68,67,69,69,7,73,74,76,79,77,74 (a) mean, 7225 (Can use -variable stats, or just compute manually) (b) median, 72 (First, rearrange the list in either increasing or decreasing order Since there is an even number of data points, there are two in the middle Take the average of the middle two) (c) mode(s), 69 and 74 (d) standard deviation, 36768579 (Use -variable stats) (e) variance (36768579) 2 = 308 of this set of data (0pts) Which of the following events is more likely to occur? Justify your answer E: Getting a six at least once in 4 throws of a single fair die F: Getting a double six at least once in 24 throws of a pair of fair dice P(E) = binompd f (4, 6,0) 577 P(F) = binompd f (24, 36,0) 494 Event E is more likely 5
2 (4pts) The chief loan officer of La Crosse Home Mortgage Company summarized the housing loans extended by the company in 204 according to type and term of the loan Her list shows that % of the loans were fixedrate mortgages (F), 25% were adjustable-rate mortgages (A), and 5% belong to some other category (O) Of the fixed-rate mortgages, 80% were 30-year loans and 20% were 5-year loans; of the adjustable-rate mortgages, 40% were 30-year loans and 60% were 5-year loans; finally, of the other loans extended, 30% were 5-year loans, 60% were 0-year loans, and 0% were for a term of 5 years or less (a) Draw a tree diagram representing the data F 8 2 30 5 7 25 A 4 6 30 05 5 O 3 6 5 0 5 (b) What is the probability that a home loan extended by La Crosse has an adjustable rate and is for a term of 5 years? P(A 5) = (25)(6) = 5 (c) What is the probability that a home loan extended by La Crosse is for a term of 30 years? P(30) = (7)(8) + (25)(4) = 66 (d) What is the probability that a 5-year loan has a fixed rate? P(F 5) = P(F 5) (7)(2) P(5) = (7)(2)+(25)(6)+(05)(3) = 6 28 459 6
3 (0pts) Four balls are selected at random without replacement from an urn containing four green balls, two red balls, and two blue balls Let the random variable X denote the number of blue balls drawn (a) Find the probability distribution of the random variable X x 0 2 P(X = x) C(2,0)C(6,4) C(8,4) = 5 C(2,)C(6,3) C(8,4) = 40 C(2,2)C(6,2) C(8,4) = 5 (b) Compute E(X) E(X) = 0( 5 40 5 ) + ( ) + 2( ) = Problem Part 9 0 2 3 Total Score 7