Into to Statistics Jeopardy

1. Into to Statistics Jeopardy Probability Probability Distn 100 100 200 200 300 300 400 400 500 500 600 600 Credits

2. Probability - 100 Which of the following is not a valid probability a.) 2/3 b.) 1/8 c.) .70 d.) 5/4 Answer

3. Probability - 200 On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess? a.) ¼ b.) ¾ c.) ½ d.) 1 Answer

4. Probability - 300 A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected, what is the probability that it is blue? a.) 1/4 b.) 1/3 c.) 1/5 d.) 1/9 Answer

5. Probability - 400 If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. a.) 31/365 b.) 1/31 c.) 1/365 d.) 1/12 Answer

6. Probability - 500 • An assignment of probability must obey which of the following? • a) The probability of any event must be a number between 0 and 1, inclusive. • b) The sum of all the probabilities of all outcomes in the sample space must be exactly 1. • c) The probability of an event is the sum of the outcomes in the sample space which make up the event. • d) All of the above. • e) A and B only. Answer

7. Probability - 600 A class consists of 61 students, 10 of which are women. If a student is chosen at random, what is the probability that the student is not a women? a.) 10/61 b.) 1/61 c.) 51/61 d.) 10/51 Answer

8. Probability - 100 Answer Which of the following is not a valid probability d.) 5/4 Probabilities are always a value between zero and 1 inclusive. Since 5/4 is greater than 1, it cannot be a valid probability.

9. Probability - 200 Answer On a multiple choice test with four possible answers for each question, what is the probability of answering a question correctly if you make a random guess? a.) ¼ The numerator in our fraction indicates the number of correct choices, the denominator is the total number of choices.

10. Probability - 300 Answer A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If a marble is randomly selected, what is the probability that it is blue? a.) 1/4 There are 3 blue marbles out of a total of 12 marbles, so the probability of drawing a blue marble is 4/12 which reduces to 1/4

11. Probability - 400 Answer If a person is randomly selected, find the probability that his or her birthday is in May. Ignore leap years. a.) 31/365 There are 31 days in May out of 365 possible birthdays. (Note: since not all months have the same number of days, we must use days instead of months to find the probability.)

12. Probability - 500 Answer • An assignment of probability must obey which of the following? • a) The probability of any event must be a number between 0 and 1, inclusive. • b) The sum of all the probabilities of all outcomes in the sample space must be exactly 1. • c) The probability of an event is the sum of the outcomes in the sample space which make up the event. • d) All of the above. • a, b, and c are all true statements

13. Probability - 600 Answer A class consists of 61 students, 10 of which are women. If a student is chosen at random, what is the probability that the student is not a women? c.) 51/61 If there are 61 students, 10 of which are women, then there must be 51 (61-10) which are not women. So the probability of not selecting a woman is 51/61

14. Probability Distn - 100 Determine whether the following is a valid probability distribution a.) Yes b.) No Answer

15. Probability Distn - 200 Determine whether the following is a valid probability distribution a.) Yes b.) No Answer

16. Probability Distn - 300 In a certain town, 60% of adults have a college degree. The accompanying table describes the probability distn for the number of adults (among 4 randomly selected adults) who have a college degree Find the probability that there are at least 2 with college degrees. a.) 0.3456 b.) 0.8208 c.) 0.4752 d.) 0.5248 Answer

17. Probability Distn - 400 Find the probability that there are less than 3 people who have college degrees. a.) 0.3456 b.) 0.8704 c.) 0.5248 d.) 0.1296 Answer

18. Probability Distn - 500 Find the expected number (the mean number) of people with college degrees from 4 randomly chosen people. Answer

19. Probability Distn - 600 Find the standard deviation for the number of people who have college degrees out of 4 randomly selected people Answer

20. Probability Distn - 100 Ans. Determine whether the following is a valid probability distribution • b.) No • 0 ≤ P(x) ≤ 1—This condition is met • ∑ P(x) = 1– The sum of the probabilities = .977 which ≠ 1---so this condition is not met and the distn is not valid

21. Probability Distn - 200 Ans. Determine whether the following is a valid probability distribution • b.) No • 0 ≤ P(x) ≤ 1—This condition is not met and the distn is not valid • ∑ P(x) = 1– The sum of the probabilities = 1

22. Probability Distn - 300 Ans. Find the probability that there are at least 2 with college degrees. b.) 0.8208 The probability of at least 2 having college degrees is found by finding the sum of 2, 3, and 4 having degrees

23. Probability Distn - 400 Ans. Find the probability that there are less than 3 people who have college degrees. c.) 0.5248 The probability of less than 3 people having college degrees is found by finding the sum of 2, 1, and 0 having degrees= .0256+.1536+.3456

24. Probability Distn - 500 Ans. To find the expected value (the mean) of the distribution μx = ∑ x •P(x) = 0(.0256) + 1(.1536) + 2(.3456) + 3(.3456) + 4(.1296)= 2.4 TI-Tips: X’s in list 1: P(x) in list 2: 1-var stats L1, L2

25. Probability Distn - 600 Ans. To find the standard deviation: σ=√∑(x-μ)2•P(x) (0-2.4)2•.0256 + (1-2.4)2•.1536 + (2-2.4)2•.3456 + (3-2.4)2•.3456 + (4-2.4)2•.1296 = .9798

26. Credits Questions have come from the Test Bank for Basic Practice of Statistics And Essentials of Statistics