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STP 226 Statistics Diane Richardson Print name here_________________________ Test #2 Summer 2015 Honor Statement: By signing below you confirm that you have neither given nor received any unauthorized assistance on this exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone until the exam testing period is over. In addition, your calculator’s memory and menus may be checked at any time and cleared by any testing center proctor or Mathematics Department instructor. _ Signature Instructions: ________________________ Date The exam is worth a total of 105 points; please make sure your exam has all pages before you begin. Make sure that you have all 10 pages to your exam. If you do not have 10 pages, then contact your Instructor. Part 1 is Free Response Show all work in detail or your answer will not receive any credit. Include appropriate units on all questions that apply. Write neatly and box all answers. Part 2 is Multiple Choice Problems 7-16 are worth 6 points and problems 17-19 are worth 4 points. Showing all work in detail will assist you in obtaining the correct answers and will be reviewed at the Instructor’s discretion. Please ask your instructor if you need scratch paper. No calculators or computers that do symbolic algebra, like the Casio FX-2, TI-89, or TI- 92, may be used. A table is given on page seven for you to write in the letter for the correct answer. You may take these pages off to help you write the correct letter in for each answer. The formulas are on page eight of the exam. The z-tables are on the last two pages of the exam. STP 226 Test 2 - Summer 2015 Page 2 Part 1 is Free Response. Make sure to show all of your work. No work, no credit. The following table displays the finishing times, in seconds, for the winners of fifteen 1 – mile thoroughbred horse races, as found in two recent issues of Thoroughbred Times [ 16 points] 94.15 93.37 82.01 95.57 97.73 101.09 99.38 97.19 96.63 101.05 83.05 97.91 98.44 97.47 95.10 If the Normal Scores in ascending order are as follows: -1.71 -1.23 -0.94 -0.33 -0.16 0 0.52 0.71 0.94 Finishing times in sec -0.71 0.16 1.23 Normal Score. A table is provided for your convenience to organize the information. 2. Construct a Normal probability plot of the data 3. Is the data normally distributed? If so why? If not, then why not? SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences -0.52 0.33 1.71 STP 226 Test 2 - Summer 2015 Page 3 Use the following information for problems 4-6 to find the requested information (18 pts) Heights in inches for the population of Five Senior/Junior players on the ASU Water Polo Team in 2013 included Player Weight Morrison (M) 67 Brightwell (B) 69 Haas (H) 70.5 Young (Y) 70 Silverberg (S) 68 With a population mean µ=68.9 inches. For a sampling distribution of size n=2 from the population of the five senior players gives mean heights in the following table Players Mean Height M,B 68 M,H M,Y 68.5 M,S 67.5 B,H 69.75 Players Mean Height B,Y 69.5 B,S 68.5 H,Y 70.25 H,S 69.25 Y,S 69 4. What is the mean height for Morrison and Haas? 5. From the sampling distribution, what is the probability that the mean height of the two players is within 1 inch of the true mean? 6. If samples of size 4 are to be chosen from the population of size 5 instead of samples of size 2, how many groups would there be? SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences STP 226 Test 2 - Summer 2015 Page 4 Part 2 Multiple Choice The hours of sleep Americans get on a typical night is shown in the table. For problems 710 use the following table to find the frequencies requested for each of the following events. Hours of Sleep 4 or less 5 6 7 8 9 10 or more Sum of Frequencies= Frequency: Number Americans in millions 12 27 75 90 81 9 6 300 A: at least 7 hours were slept. C: at most 5 hours were slept. B: exactly 6 hours were slept. D: at most 8 hours were slept. 7. Event A A) 15 B) 285 C) 114 D) 186 E) None of the Above 8. Events (D or C) A) 15 B) 285 C) 246 D) 324 E) None of the Above B) 186 C) 15 D) 285 E) None of the Above B) 0 C) 114 D) 100 E) None of the Above 9. Event ( not D) A) 114 10. Event ( B and C) A) 153 SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences STP 226 Test 2 - Summer 2015 Page 5 A recent study on college students found that 15% smoke, 7.9% have been diagnosed as having depression, and 5.27% are depressed smokers. For a college student selected at random, let S be the event that the person is a smoker, and D be the event that the person has been diagnosed as been depressed. For problems 11 and 12, find the following probabilities: 11. The probability that the student is a smoker or has been diagnosed with depression. A) 0.242 B) 0.229 C) 0.71 D) 0.1763 E) None of the Above 12. Find the probability that the person was a non-smoker. A) 0.921 B) 0.85 C) 0.9473 D) 0.771 E) None of the Above In questions 13 - 14 use the tables of the standard normal curve to give the 4 decimal place answer for the area or the 2 decimal place answer for the z-scores. 13. Find the area between 1.25 and 2.13 under N(0,1) A) 0.8944 B) 0.089 C) 0.1056 D) 0.911 E) None of the Above 14. Find the 40th percentile of the standard normal curve. A) 0.60 B) 0.25 C) -0.25 D) -0.60 E) None of the Above SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences STP 226 Test 2 - Summer 2015 Page 6 Weights of a Beagle dog . Use the following information for answering the questions below: The data for this example is for the full grown dog breed known as the Beagle (think Snoopy). The weight of this breed is normally distributed with a mean of 22.5 pounds and a standard deviation of 2.2 pounds. Use this information to answer questions 15. Compute the probability that a dog will weigh less than 21.2 pounds A 0.59 B 0.7224 C 0.2776 D 0.41 E None of the Above 16. If four Beagle dogs are randomly selected what is the probability that the sample mean X of the four, Beagle dogs more than 24.5 pounds? A. 0.6372 B. 0.9656 C. 0.8186 D. 0.0344 E. None of these Short Answer. 17. Normal probability plots are used to determine if a data set has outliers. A) True B) False 18. We can use symbolic notation z 0.20 for 80th percentile of N(0,1) distribution A) True B) False 19. Suppose the median home value (house or condo) in Tempe, Arizona is $203,000 in 2013 is right skewed. For the samples of size 64, sample mean x has an approximately normal distribution. A. True B. False SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences STP 226 Test 2 - Summer 2015 Page 7 Circle your answer choice on the exam AND fill in the answer with the letter of the answer that you believe is the correct answer. Problem Number Letter of Answer 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. XXXXXXXXX XXXXXXXXXX 17. 18. 19 SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences STP 226 Test 2 - Summer 2015 Page 8 Formulas Exam 2 Probability Rules f P( E ) n P(not E ) 1 P( E ) P( A or B ) P( A) P( B) P( A and B ) n! n Cr n - r ! r ! x Descriptive Measures: z x n x- x N Sampling Distribution of X : x , x Standardized version of X : z n , x n SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences STP 226 Test 2 - Summer 2015 SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences Page 9 STP 226 Test 2 - Summer 2015 SU2015B © 2015 Arizona State University, School of Mathematics and Statistical Sciences Page 10