Math 140: Test #2 Spring 2010 Page 1 of 5 Math 140: Statistics Your Name ______________________ Test 2, April 13, 2010 1. (16 pts.) In a hypothetical of a group of students, the following results were obtained: Midterm Exam = 80 points, SD = 10 points Final Exam = 85 points, SD = 5 points r = 0.8 a) Estimate the exam score for those that made 80 points on the midterm b) Estimate the exam score for those that made 95 on the midterm c) Estimate the midterm score for those that made 90 on the final d) Estimate the percentile rank for the final for those in the 80th percentile for the midterm 2. (2 pts.) As part of their training, pilots make two practice landings. Analysis shows those that did well on the first tended to do worse of the second and those that did poorly on the first did well on the second. Command concluded that praise for the first landing made the pilots overconfident while criticism improved their performance. Give an alternative explanation based on the material we have studied.Math 140: Test #2 Spring 2010 Page 2 of 5 3. (16 pts.) In a hypothetical study, the following results were obtained: Avg. Husband’s Education = 14 years, SD = 2 years Avg. Wife’s Education = 15 years SD = 1 years r = 0.5 Assume that you are using the husband’s education to predict the wife’s education. a) What is the slope of the regression line? b) What is the intercept of the regression line? c) Write the equation of the regression line. d) Use the regression line to estimate the education for the wife of a man who has completed 18 years of school. Show your work! 4. (3 pts.) For the following box, say whether color and number are dependent or independent. 1 2 2 1 1 2Math 140: Test #2 Spring 2010 Page 3 of 5 5. (12 pts.) A deck of cards is shuffled and three cards are dealt. a) What is the probability that the first card is an ace? b) What is the probability that the second card is an ace? c) What is the probability that the second card is an ace given that the first card is a king? d) What is the probability that the first card is an ace and the second card is an ace? e) What is the probability that the second card is an ace given that the first card is an ace? f) What is the probability that all three cards are aces? 6. (9 pts.) A pair of dice is rolled. a) What is the probability of getting two sixes? b) What is the probability of not getting any sixes? c) What is the probability of getting at least one six?Math 140: Test #2 Spring 2010 Page 4 of 5 7. (9 pts.) A box contains 20% red and 80% blue marbles. You are drawing with replacement. a) You win a suitcase full of money if there are more than 22% red marbles in your draw. Which is better: 10 draws or 100 draws? b) You win a suitcase full of money if exactly 80% of the draws are blue marbles. Which is better: 10 draws or 100 draws? c) You win a suitcase full of money if between 18% and 24% of the marbles drawn are red. Which is better: 10 rolls or 100 rolls? 8. (9 pts.) You make 100 draws with replacement from this box: 5 tickets –$20 5 tickets $10 10 tickets with $5 a) What is the most you can win? b) What is the most you can lose? c) How much do you expect to win or lose? 9. (4 pts.) Find the standard deviation for the following set of data using the short-cut method presented in your book: 5, 5, 5, 2, 2, 2Math 140: Test #2 Spring 2010 Page 5 of 5 10. (12 pts. total) You are drawing 100 draws with replacement from the following box: 0 0 0 0 5 a) (2 pts.) What is the average for the box? b) (2 pts.) What is the SD for the box? c) (2 pts.) What is the expected value for the experiment? d) (2 pts.) What is the standard error for the experiment? e) (4 pts.) What is the probability that the sum of the draws is greater than 90? 11. (8 pts) For the preceding problem, a) what is the probability of drawing exactly 20 fives? (Hint: What does the box model look like?) b) what is the probability of drawing between 19 and 21 fives inclusive? Pledged: