ANSWER SHEET FINAL EXAM MATH 111 SPRING 2009 FRIDAY 1 MAY 2009 LAST NAME: (PRINT ABOVE IN LARGE CAPITALS) CIRCLE LECTURE HOUR 10AM 2PM FIRST NAME: (PRINT ABOVE IN CAPITALS) CIRCLE LAB DAY: TUESDAY THURSDAY ***** ***** CIRCLE AT MOST ONE LETTER FOR YOUR FINAL ANSWER TO EACH QUESTION ON THIS ANSWER SHEET BELOW 1. A B C D E 11. A B C D E 2. A B C D E 12. A B C D E 3. A B C D E 13. A B C D E 4. A B C D E 14. A B C D E 5. A B C D E 15. A B C D E 6. A B C D E 16. A B C D E 7. A B C D E 17. A B C D E 8. A B C D E 18. A B C D E 9. A B C D E 19. A B C D E 10. A B C D E 20. A B C D E
FINAL EXAM MATH 111 SPRING 2009 FRIDAY 1 MAY 2009 LAST NAME: (PRINT ABOVE IN LARGE CAPITALS) CIRCLE LECTURE HOUR 10AM 2PM 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.
1. In Duckburg there is always a 60 percent chance of rain and whenever it is raining there is always a 25 percent chance of a tornado. Then in duckburg, the percentage chance of both rain and a tornado simultaneously is always (A) 15 (B) 30 (C) 25 (D) 85 (E) NONE OF THESE 2. Both Mickey and Donald are running for Town Council of Duckburg. There is a 40 percent chance that Mickey will be elected to the council and a 30 percent chance that Donald will be elected to the council, but only a 10 percent chance that both will be elected to the council. The percentage chance that at least one of the two but not both will be elected to the Duckburg Town Council is (A) 60 (B) 50 (C) 40 (D) 30 (E) NONE OF THESE 3. The chance of a dust storm in Duckburg is always 30 percent and the chance of a rain storm in Duckburg is always 60 percent, but the chance of at least one of these storms is always 70 percent. If both of these storms happen simultaneously the result is a mud storm. The chance of a mud storm in Duckburg is always (A) 50 (B) 40 (C) 30 (D) 20 (E) NONE OF THESE 4. If the unknown number X is normally distributed with mean 70 and standard deviation 10, then the probability that X is between 65 and 80 is (A).191 (B).533 (C).625 (D).433 (E) NONE OF THESE 5. If the unknown number X is normally distributed with mean 70 and standard deviation 10, then the probability that X is more than 65 is (A).691 (B).191 (C).309 (D).500 (E) NONE OF THESE
6. If the unknown number X is normally distributed with mean 70 and standard deviation 10, then the probability that X is less than 85 given that it is more than 65 is (A).691 (B).625 (C).901 (D) 2.03 (E) NONE OF THESE 7. On average, 24-7, trolleys arrive at my trolley stop at the rate of 6 per hour, independent of the time of day. We assume that the number of trolleys arriving in nonoverlapping time intervals are independent of each other. If I arrive at my trolley stop at 6PM and watch the trolleys go by until 9PM, what is the chance I will see exactly 17 trolleys arrive at my trolley stop? (A).0936 (B).0909 (C).469 (D).655 (E) NONE OF THESE 8. On average, 24-7, trolleys arrive at my trolley stop at the rate of 6 per hour, independent of the time of day. We assume that the number of trolleys arriving in nonoverlapping time intervals are independent of each other. If I arrive at my trolley stop at 6PM, what is the chance I must wait more than 15 minutes for a trolley? (A).00249 (B).0149 (C).0498 (D).223 (E) NONE OF THESE 9. On average, 24-7, buses arrive at my bus stop at the rate of 16 per hour, independent of the time of day. We assume that the number of buses arriving in non-overlapping time intervals are independent of each other. What is the standard deviation in the number of buses arriving per hour? (A) 16 (B) 6 (C) 4 (D) 2 (E) NONE OF THESE 10. Mickey Mouse is using his radar gun to check for speeders passing by his home in Duckburg. He already knows that always 35 percent of the passing traffic is speeding. If he measures the speed of the next 100 passing vehicles, what is the chance he will find no more than 32 are speeding? (A).173 (B).303 (C).320 (D).914 (E) NONE OF THESE
11. Uncle Scrooge gives Mickey a chance to win some money on his birthday. He puts 100 envelopes in a box, each containing a single check drawn on Duckburg National Bank and allows Mickey to choose 10 of the envelopes from the box. Ten of the envelopes in the box each contain a check for ten thousand dollars. Fifteen of the envelopes in the box each contain a check in the amount of five thousand dollars, and all the rest each contain a check for one thousand dollars. What is the total amount of money Mickey should expect to win, expressed in thousands of dollars? (A) 2.5 (B) 25 (C) 250 (D) 500 (E) NONE OF THESE 12. Uncle Scrooge gives Mickey a chance to win some money on his birthday. He puts 100 envelopes in a box, each containing a single check drawn on Duckburg National Bank and allows Mickey to choose 10 of envelopes from the box. Ten of the envelopes in the box each contain a check for ten thousand dollars. Fifteen of the envelopes in the box each contain a check in the amount of five thousand dollars, and all the rest each contain a check for one thousand dollars. Mickey draws the envelopes from the box one after another. What is the percentage chance the third envelope contains at least 5 thousand dollars? (A) 5 (B) 15 (C) 25 (D) 75 (E) NONE OF THESE 13. Uncle Scrooge gives Mickey a chance to win some money on his birthday. He puts 100 envelopes in a box, each containing a single check drawn on Duckburg National Bank and allows Mickey to choose 10 of envelopes from the box. Ten of the envelopes in the box each contain a check for ten thousand dollars. Fifteen of the envelopes in the box each contain a check in the amount of five thousand dollars, and all the rest each contain a check for one thousand dollars. Mickey draws the envelopes from the box one after another, WITHOUT REPLEACEMENT. What is the probability that exactly three of the ten drawn envelopes contain at least 5 thousand dollars? (A).264 (B).776 (C).250 (D).130 (E) NONE OF THESE
14. Donald is studying the length of rainbow trout in Lake Duckburg, which he assumes to be normally distributed. In a sample of 15 trout he finds that the average length is 14 inches with a standard deviation of 2.4 inches. Based on this data, what is the MARGIN OF ERROR of the 95 percent confidence interval for the true population mean length for rainbow trout in Lake Duckburg. (A) 1.845 (B) 1.60 (C) 1.329 (D) 1.215 (E) NONE OF THESE 15. Donald is studying the length of rainbow trout in Lake Duckburg, which he assumes to be normally distributed. In a sample of 15 trout he finds that the average length is 14 inches with a standard deviation of 2.4 inches. What is the significance of this data as evidence that the true population mean length of rainbow trout in Lake Duckburg exceeds 13 inches? (A).0644 (B).0533 (C).0422 (D).0311 (E) NONE OF THESE 16. Donald has decided to take a large enough sample to make the margin of error in a 99 percent confidence interval for true population mean length of rainbow trout in Lake Duckburg to be no more than one quarter of an inch. He knows that length for the population of rainbow trout in Lake Duckburg is normally distributed with standard deviation at most 5 inches. Based on this information, what is the smallest possible sample that will suffice for this confidence interval Donald wants to make? (A) 1537 (B) 1633 (C) 2637 (D) 2654 (E) NONE OF THESE 17. Suppose that the length of rainbow trout in Lake Duckburg is normally distributed with mean 12 inches and standard deviation 3 inches. Donald catches 5 of these rainbow trout and lines them up nose to tail on the dock and measures the length from the tail of the last fish in line to the nose of the front fish in the line. What is the probability that this length measures between 65 and 70 inches? (A).168 (B).117 (C).0474 (D).0371 (E) NONE OF THESE
18. Goofy is running for Mayor of Duckburg and the election is tomorrow. He asks 12 people selected at random if they will vote for him and only 4 say yes. What is the P-value of this sample data as evidence that Goofy will lose the election? (A).114 (B).138 (C).333 (D).389 (E) NONE OF THESE 19. Mickey is testing rope to go mountain climbing on Mount Duckburg. He has decided that he will work at level of significance.00001. The significance of his data as evidence that the rope exceeds his minimum strength requirements is.000234. He should (A) conclude that his rope is just barely strong enough and therefore he can use it for mountain climbing. (B) conclude that he has made a type I error and therefore the rope is really OK. (C) conclude there must have been an error in the calculation of the sample standard deviation. (D) conclude that he has made a type II error for which there is no excuse. (E) NONE OF THESE 20. If we test the null hypothesis H 0 : µ 1000 at level of significance.05, then (A) there is a 5 percent chance that we will think µ 1000. (B) there is a 5 percent chance that we will think µ 1000 when in fact µ.05. (C) there is a 5 percent chance that we will think that µ 1000 when in fact µ < 1000. (D) there is a 5 percent chance that we will think that µ < 1000 when in fact µ 1000. (E) NONE OF THESE