1. Advanced Math Topics Chapter 6 Review Olympics

2. One sheet per player Make an answer column on the left hand side of your sheet Work together to solve each question Winning team earns a reward We will go over the process and answers for each

3. BRONZE 1 point

4. 1)Find the missing probability. xp(x) 0? 10.23 20.08 30.04 40.44

5. 2) Find the mean of the probability distribution. xp(x) 00.1 1 2 30.2 40.15 50.3 60.05

6. 3) 45% of college applicants into the UC system are accepted. If there are 200,000 applicants, how many can be expected to be accepted? What is the standard deviation. Round to the nearest hundredth.

7. 4) If the variance of a probability distribution is 3.457, what is the standard deviation? Round to the nearest hundredth.

8. SILVER 2 points

9. 5) Find the standard deviation to the nearest hundredth. xp(x) 00.11 10.21 20.4 30.12 40.10 50.04 60.02

10. 6) The probability that a customer at a gas station purchases diesel is 0.15. If six drivers pull into a gas station, find the probability that exactly 2 of them purchase diesel. Round to the nearest hundredth of a percent.

11. 7) The number of particles emitted from a radioactive source has an average of 4 particle per minute. Find the probability that exactly 2 are emitted. Round to the nearest hundredth of a percent.

12. 8) A package of mixed nuts contains 20 walnuts and 80 almonds. Five are grabbed in one handful. Find the probability that exactly one is a walnut. Round to the nearest hundredth of a percent.

13. GOLD 3 points

14. 9) Men’s Wearhouse got a shipment of 90 suits. Eight of them are missing shoes. You randomly grabbed 6 suits. Find the probability that at least 5 have shoes. Round to the nearest hundredth of a percent.

15. 10) According to police statistics, only 71% of crimes go reported. If ten crimes are randomly selected, find the probability that at most 2 are not reported. Round to the nearest hundredth of a percent.

16. Rows 1 and 2 Trade Papers Rows 3 and 4 Trade Papers Rows 5 and 6 Trade Papers Score only one sheet, then add it to their teammate’s score. Points: Gold = 3 Silver = 2Bronze = 1 If there is more than 1 part, all parts must be correct to get the points

17. BRONZE 1 point

18. 1)Find the missing probability. xp(x) 0? 10.23 20.08 30.04 40.44 Answer: 0.21 Process: The probabilities must add to 1.

19. 2) Find the mean of the probability distribution. xp(x) 00.1 1 2 30.2 40.15 50.3 60.05 Answer: 3.3 Process: Summate x times p(x).

20. 3) 45% of college applicants into the UC system are accepted. If there are 200,000 applicants, how many can be expected to be accepted? What is the standard deviation. Round to the nearest hundredth. Answer: 90,000 and 222.49 Process: Multiply n(p) to find the average. Multiply n(p)(q) and take the square root to find the standard deviation.

21. 4) If the variance of a probability distribution is 3.457, what is the standard deviation? Round to the nearest hundredth. Answer: 1.86 Process: Square root the variance

22. SILVER 2 points

23. 5) Find the standard deviation to the nearest hundredth. xp(x) 00.11 10.21 20.4 30.12 40.10 50.04 60.02 Answer: 1.36 Process: There are 2 methods. The more common method is to summate x 2 p(x) and then subtract μ 2. Then, square root.

24. 6) The probability that a customer at a gas station purchases diesel is 0.15. If six drivers pull into a gas station, find the probability that exactly 2 of them purchase diesel. Round to the nearest hundredth of a percent. Answer: 17.62% Process: Since the probabilities are independent… Use the binomial distribution formula. 6 C 2 (0.15) 2 (0.85) 4

25. 7) The number of particles emitted from a radioactive source has an average of 4 particle per minute. Find the probability that exactly 2 are emitted. Round to the nearest hundredth of a percent. Answer: 14.65% Process: Since there is an average over a given region or period of time, use the Poisson formula.

26. 8) A package of mixed nuts contains 20 walnuts and 80 almonds. Five are grabbed in one handful. Find the probability that exactly one is a walnut. Round to the nearest hundredth of a percent. Answer: 42.01% Process: Since there is no replacement, use the hypergeometric formula. (20 choose 1)(80 choose 4) divided by (100 choose 5).

27. GOLD 3 points

28. 9) Men’s Wearhouse got a shipment of 90 suits. Eight of them are missing shoes. You randomly grabbed 6 suits. Find the probability that at least 5 have shoes. Round to the nearest hundredth of a percent. Process: P(5 have shoes) + P(6) since you cannot choose more than 6 with shoes. Since there is no replacement, use the hypergeometric formula for P(5) and P(6). Answer: 91.30%

29. 10) According to police statistics, only 71% of crimes go reported. If ten crimes are randomly selected, find the probability that at most 2 are not reported. Round to the nearest hundredth of a percent. Answer: 40.99% Process: Since the probabilities are independent… Use the binomial distribution formula for p(0) + p(1) + p(2) are not reported.

30. Answer:11.06% Tiebreaker) The probability of getting on the Wall of Fame is 0.04. You randomly select 3 people from the class, find the probability exactly one person made the Wall of Fame. Say your answer as a percent rounded to the nearest hundredth of a percent.

31. HW P. 347 #1-11 (Skip 4, 9, 10) To study, look at this slideshow, past slideshows, the book, the chapter review, etc. Winners: Odds Test Tomorrow