FINAL EXAM MATH 111 FALL 2009 TUESDAY 8 DECEMBER AM-NOON

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1 FINAL EXAM MATH 111 FALL 2009 TUESDAY 8 DECEMBER AM-NOON ANSWERS***** 1. (B) (A) 0 3. (C) (E) NONE OF THESE 5. (D) 4/9 6. (A) (B) (D) (A) (D) (C) (C) (D) (D) (A) (B) (C) (B) (D) (C) (C) (C) (E) NONE OF THESE 24. (A) BINOMIAL 25. (B) YES IT DOES

2 ANSWER SHEET FINAL EXAM MATH 111 FALL 2009 TUESDAY 8 DECEMBER AM-NOON LAST NAME: (PRINT AT TOP IN LARGE CAPITALS) FIRST NAME: (PRINT ABOVE IN CAPITALS) CIRCLE LAB DAY: TUESDAY THURSDAY CIRCLE LECTURE HOUR: 11AM 11AM ***** ***** CIRCLE AT MOST ONE LETTER FOR YOUR FINAL ANSWER TO EACH QUESTION ON THIS ANSWER SHEET BELOW 1. A B C D E 13. A B C D E 2. A B C D E 14. A B C D E 3. A B C D E 15. A B C D E 4. A B C D E 16. A B C D E 5. A B C D E 17. A B C D E 6. A B C D E 18. A B C D E 7. A B C D E 19. A B C D E 8. A B C D E 20. A B C D E 9. A B C D E 21. A B C D E 10. A B C D E 22. A B C D E 11. A B C D E 23 A B C D E 12. A B C D E 24 A B C D E 25. A B C D E

3 FINAL EXAM MATH 111 FALL 2009 TUESDAY 8 DECEMBER AM-NOON LAST NAME: (PRINT AT TOP IN LARGE CAPITALS) FIRST NAME: (PRINT ABOVE IN CAPITALS) CIRCLE LAB DAY: TUESDAY THURSDAY ***** ***** RULES: You are permitted to have a calculator and writing instruments. No books or notes allowed. Exam is conducted under Tulane honor code; all work is to be your own. Do all work on the backs and sides of this exam; CIRCLE your answers in the indicated spaces AND ON THE ANSWER SHEET PROVIDED (ATTACHED TO THE EXAM). BE SURE TO FILL IN ALL OF THE IDENTIFICATION INFORMATION ASKED FOR CORRECTLY AS DIRECTED AND PRINT YOUR NAME IN LARGE CAPITAL LETTERS ON THE TOP OF EACH PAGE OF THE EXAM AND FILL IN ALL THE IDENTIFICATION INFORMATION REQUIRED ON THE ANSWER SHEET INCLUDING YOUR NAME IN LARGE CAPITAL LETTERS. ANSWERS SHOULD BE CORRECT TO THREE SIGNIFICANT DIGITS. WARNING: Failure to follow the above rules and previous identification directives may result in your receiving a final grade of F for the course.

4 ANSWERS***** 1. (B) (A) 0 3. (C) (E) NONE OF THESE 5. (D) 4/9 6. (A) (B) (D) (A) (D) (C) (C) (D) (D) (A) (B) (C) (B) (D) (C) (C) (C) (E) NONE OF THESE 24. (A) BINOMIAL 25. (B) YES IT DOES

5 In Lake Wobegon, 25 percent of the trout weigh more than twenty pounds and 80 percent of the trout that weigh over twenty pounds are over fifteen inches long. But, only one third of the trout that weigh under twenty pounds are over fifteen inches long. Let A denote the event a randomly selected trout from Lake Wobegon weighs more than twenty pounds, and let B denote the event that a randomly selected trout from Lake Wobegon is over fifteen inches long. 1. What is the probability that a trout in Lake Wobegon both weighs over twenty pounds and is over fifteen inches long, or, in symbols, what is P (A & B)? (A).15 (B).20 (C).25 (D).33 (E) NONE OF THESE 2. What is the probability that a trout taken from Lake Wobegon is found to weigh exactly twenty pounds? (A) 0 (B).01 (C).25 (D) indeterminate (E) NONE OF THESE 3. What is the probability a trout taken from Lake Wobegon is over fifteen inches long, or in symbols, what is P (B)? (A).25 (B).35 (C).45 (D).75 (E) NONE OF THESE 4. What is the probability that a trout in Lake Wobegon is both shorter than fifteen inches in length and weighs under twenty pounds, or in symbols, P ([not A] & [not B])? (A).15 (B).85 (C).20 (D).25 (E) NONE OF THESE 5. Given that a trout taken from Lake Wobegon is longer than fifteen inches, what is the probability it weighs over twenty pounds? (A) 1/9 (B) 2/9 (C) 1/3 (D) 4/9 (E) NONE OF THESE

6 A sample of 18 trout from Lake Wobegon was found to have a sample mean weight of 17.8 pounds with a sample standard deviation of 1.6 pounds. Assume that Lake Wobegon trout weight is normally distributed. 6. Based on this sample, what is the MARGIN OF ERROR for the 95 percent confidence interval for the true mean weight of trout in Lake Wobegon? (A).796 (B).739 (C) 18.6 (D) 18.5 (D) NONE OF THESE 7. What is the significance or P-value of this data as evidence that the true mean weight of trout in Lake Wobegon exceeds 17 pounds? (A).0169 (B).0244 (C).0489 (D).976 (E) NONE OF THESE 8. If Sam also assumes that the population standard deviation in weight of trout in Lake Wobegon is 1.9 pounds, then what would be the MARGIN OF ERROR for Sam s 99 percent confidence interval for true mean weight of trout in Lake Wobegon? (A) (B) (C) 19.0 (D) (E) NONE OF THESE Suppose X is normally distributed with mean E(X) = 2 and standard deviation σ X = What is the probability that X is between -3 and 4? (A).375 (B).377 (C).423 (D).380 (E) NONE OF THESE 10. If x is a number with the property that P (X x) =.85, then what is x? (A) (B) (C) 8.50 (D) 9.26 (E) NONE OF THESE 11. If Y is the average of 5 independent observations of X, then what is the probability that Y is between 1 and 5? (A).746 (B).223 (C).456 (D) indeterminate (E) NONE OF THESE

7 A box is filled with 100 envelops containing cash. Of the 100 envelops in the box, exactly 70 each contain a single one dollar bill, exactly 15 each contain a single five dollar bill, exactly 10 each contain a single ten dollar bill, exactly 4 contain a single twenty dollar bill, and exactly one envelop contains a single one hundred dollar bill. 12. If we randomly draw an envelop from the box, then how many dollars should we expect to get? (A) 1.00 (B) 4.00 (C) 4.25 (D) 5.00 (E) NONE OF THESE 13. If we randomly draw 20 envelops from the box WITHOUT REPLACEMENT, then how many dollars total should we expect to get? (A) 20 (B) 24 (C) 65 (D) 85 (E) NONE OF THESE I know that on average, 24 hours a day and 7 days a week, trolleys arrive at my trolley stop at the rate of 10 per hour, independent of the time of day. I assume that the number of trolleys arriving in non-overlapping time intervals are independent of each other. I plan to arrive at my trolley stop at 6PM and count the trolleys going by until 9PM. Let T be the number of trolleys I will count. 14. Beforehand, as I am making plans to go to the trolley stop, how many trolleys should I be expecting to count? (A) 6 (B) 10 (C) 20 (D) 30 (E) NONE OF THESE than 26? 15. What is the probability that the number T of trolleys I count will be no more (A).267 (B).0590 (C).0589 (D).233 (E) NONE OF THESE

8 Sam knows his box contains 15 RED blocks and 10 BLUE blocks. Sam allows me to draw 12 blocks from his box one after another. Sam does not see me do this, and moreover Sam does not see or know the outcome. Also, Sam does not know whether I draw with replacement or without replacement, but he does assume that I drew exactly 12 blocks from his box. Let R be the number of red blocks I draw. 16. How many of the 12 blocks I draw should Sam EXPECT are red, given the information he has? (A) 7.00 (B) 7.20 (C) 8.00 (D) CANNOT BE DETERMINED (E) NONE OF THESE 17. If Sam ASSUMES I am drawing WITH REPLACEMENT, what should he think is the value of σ R, the standard deviation of R? (A) 7.00 (B) (C) (D) (E) NONE OF THESE 18. If Sam ASSUMES I am drawing WITH REPLACEMENT, then what should he think is the probability that exactly 7 of the blocks I draw are red? (A).1429 (B).2270 (C).3118 (D).4667 (E) NONE OF THESE 19. If Sam ASSUMES I am drawing WITHOUT REPLACEMENT, what should he think is the value of σ R, the standard deviation of R? (A) 7.00 (B) (C) (D) (E) NONE OF THESE 20. If Sam ASSUMES I am drawing WITHOUT REPLACEMENT, what should he think is the probability that exactly 7 of the blocks I draw are red? (A).1429 (B).2270 (C).3118 (D).4667 (E) NONE OF THESE

9 We have decided that to be safe we must test rope for mountain climbing at significance level We assume that rope breaking strength is normally distributed. We also assume that there is a 70 percent chance a piece of rope purchased from the Duckburg Hardware Store will test strong enough for mountain climbing. We buy a batch of rope from that hardware store and tomorrow we will test 15 pieces of it. Let R be the number of pieces in the sample that will be found strong enough for mountain climbing. 21. What is the expected value of R, the number of pieces in our sample that will actually be found to be strong enough for mountain climbing? (A) 11.5 (B) 11 (C) 10.5 (D) 10 (E) NONE OF THESE 22. What is the standard deviation of R, the number of pieces in our sample that will actually be found to be strong enough for mountain climbing? (A).210 (B).458 (C) (D) 3.15 (E) NONE OF THESE 23. If tomorrow the P-Value of our sample data turns out to be.29999, then we should (choose the best ending) (A) conclude that percent of the hardware store rope is definitely defective, so we must look elsewhere for suitable mountain climbing rope. (B) conclude we can use the rope from the hardware store for mountain climbing and be glad we found rope with such a high P-Value, as that is so hard to find in hardware store rope. (C) conclude that only.001 percent of the hardware store rope is defective while the rest is stronger than we require for mountain climbing, so we can definitely use the rope for our mountain climbing. (D) conclude that percent of the hardware store rope is actually strong enough for mountain climbing so we can use this batch of rope for mountain climbing as long as we are very very careful. (E) NONE OF THESE

10 In Duckburg, a political poll (independent random sample) of registered voters will be taken today, and we use X to denote the number in the sample who will vote for Donald for Mayor of Duckburg if the election were to be held today. 24. What is the true distribution of X? (A) BINOMIAL (B) POISSON (C) UNIFORM (D) UNKNOWN (E) NONE OF THESE 25. At the.025 level of significance, if X = 9653, does this show that less than 49 percent of the registered voters would vote for Donald for Mayor of Duckburg if the election were held today? (A) DATA IS INCONCLUSIVE (B) YES IT DOES (C) IT PROVES HE WILL WIN (D) IT PROVES WE NEED ANOTHER SAMPLE (E) NONE OF THESE

FIRST NAME: (PRINT ABOVE (UNDERNEATH LAST NAME) IN CAPITALS)

ANSWER SHEET FINAL EXAM MATH 111 SPRING 2010 FRIDAY 30 APRIL 2010 8AM-NOON LAST NAME: (PRINT AT TOP IN LARGE CAPITALS) FIRST NAME: (PRINT ABOVE (UNDERNEATH LAST NAME) IN CAPITALS) CIRCLE LAB DAY: TUESDAY