1. Follow-Up on Yesterday’s last problem. Then we’ll review. Sit in the groups below Brendan and Tim are playing in an MB golf tournament. Their scores vary as they play the course repeatedly. Tim’s score X has the N(110, 10) distribution. Brendan’s score Y varies from round to round according to the N(100, 8) distribution. If they play independently, what is the probability that Tim will score lower than Brendan and thus do better in the tournament? We found the distribution of X – Y to be N(10, 12.80) We want to find the Probability that Tim’s score is less than Brendan’s (i.e. P(X<Y) which is the same as the P(X-Y<0). Let’s use a z-score the determine this probability.

2. Ways to Review Read. Reread either parts of the chapters or the 5 steps to a 5 lesson. Look over the problems that we do in class today and on the review game. Make sure that your HW is completed (HW 34-39 will be collected). Check solutions online. Doing some extra review problems won’t hurt either. Make sure that you bring your formula sheet to the test tomorrow.

3. Part 1: Review Problem Set Get in the following groups. I split you up so you would work with people that you might not normally work with. It was randomly assigned though. Look at the MC review set from 5 steps to a 5. Same set that was assigned last night. Work with your group to answer all of the multiple choice questions that you did not do last night. Also complete the following Free Response Questions: 6, 9, 12 Your team has an answer sheet on your desk as well. We will then play a review game for the last half of class.

4. Review Game for a HW Pass!

5. Review Game: Question 1

6. Answer: A Key Concept: The sample space is what is possible in a situation.

7. Review Game: Question 2

8. Answer: A Key Concept: Be careful with percents and decimals. To turn a decimal to a percent, move the decimal two spaces to the right.

9. Review Game: Question 3

10. Answer: C Key Concept: The probability is 50% (0.2 + 0.3) so over the long run we would expect approx this proportion

11. Review Game: Question 4

12. Answer: C Key Concept: P(pink U no fragrance) = 120/400 + 134/400 – 16/400 Don’t forget to subtract the “overlap” they are not mutually exclusive.

13. Review Game: Question 5

14. Answer: C Key Concept: independence means that the probability of A does not impact the prob. of B.

15. Review Game: Question 6

16. Answer: B Key Concept: The prob that a doctor doesn’t carry malpractice insurance is 0.18. Because of independence, if we want to calculate the prob that all 3 doctors do carry insurance, The calculation would be 0.82*0.82*0.82 = 0.82 3 = 0.551 all the rest of the time at least one doctor Does NOT carry insurance So the prob that at least one of the 3 doctors does NOT carry insurance would be 1 – 0.551 = 0.449

17. Review Game: Question 7

18. Answer: B Key Concept: In the first deck, the prob is not independent. Getting a red card on the first Card impacts (lowers) the prob of getting a red card on the second draw (12/51 as opposed To 13/52 with the first card). The probabilities are 13/52 for both red cards on the second deck.

19. Review Game: Question 8

20. Answer: B Key Concept: discrete means countable. Continuous means not countable

21. Review Game: Question 9

22. Answer: A Key Concept: Expected value is the sum of X*p(x). Make a table with outcomes and prob. 2(0.3) + 4 (0.1) + 0 (0.6) = 1

23. Review Game: Question 10 Answer: B Key Concept: 0.4 + 0.1 = 0.5

24. Review Game: Question 11

25. Answer: C Key Concept: The mean of X is 1.5. Take each x-value and subtract the mean. Then square that Value and multiply it by P(x) for each data point. Find the sum (which is the variance). Take the square Root for the std. deviation. (0-1.5) 2 (0.1) + (1-1.5) 2 (0.4)… etc. Then take the square root.

26. Review Game: Question 12

27. Answer: C Key Concept: Density curves have areas of 1. So the ten minutes must have a height of 0.1 (since 10*0.1=1). Therefore the P(6 < X < 8) = 2 *0.1 = 0.2

28. Review Game: Question 13

29. Answer: B Key Concept: remember, we can’t just add or subtract std. deviations. We can only use the rule For variances. So the variance is 1.2 2 = 1.44. The variance of X-Y = var 2 + var 2 = 1.2 2 + 1.2 2 = 2.88. The square root of this is the std deviation = 1.6970

30. Review Game: Question 14

31. Answer: A Key Concept: The mean of c = 500 + 10(200) using the rules for means. To find the standard deviation of C, use the rules for variances. The variance of X is 400. So b 2 (variance) = 10 2 400 = 40,000 the square root of this is 200.

32. Review Game: Question 15

33. Answer: C Key Concept: For standard deviation we would need to know if X and Y were independent before We could do part c.

34. Review Game: Question 16

35. Answer: C Key Concept: Calculate a z-score and look it up on the z-table. (700-530)/120= z = 1.416. Prob from the z-table is 0.922. We want it to EXCEED $700 so we are looking for the right tail. So we do 1- 0.922 = 0.0778

36. Review Game: Question 17

37. Answer: B Key Concept: Find the expected value 1(0.1) + 2(0.2) + 3(0.3) + 4(0.2) + 5(0.1) + 6(0.1)