Skills Check

Skills Check

Question 8.1

1. You read in a book on poker that the probability of being dealt three of a kind in a five-card poker hand is . What does this mean?

388

  1. If you deal thousands of poker hands, the fraction of them that contain three of a kind will be very close to .
  2. If you deal 50 poker hands, exactly one of them will contain three of a kind.
  3. If you deal 10,000 poker hands, exactly 200 of them will contain three of a kind.

1.

a

Question 8.2

2. If two coins are flipped and then a die is rolled, the sample space would have ____________ different outcomes.

Skills Checks 3–7 use this model for the blood type of a randomly chosen person in the United States:

Blood type O A B AB
Probability 0.45 0.40 0.11 ?

2.

24

Question 8.3

3. The probability that a randomly chosen American has type AB blood is

  1. 0.044.
  2. 0.04.
  3. 0.4.

3.

b

Question 8.4

4. María has type A blood. She can safely receive blo transfusions from people with blood types O or A. The probability that a randomly chosen American can dona blood to María is __________.

4.

0.85

Question 8.5

5. What is the probability that a randomly chosen American does not have type O blood?

  1. 0.55
  2. 0.45
  3. 0.04

5.

a

Question 8.6

6. A random sample of two Americans is selected. What is the probability that both will have type O blood?

  1. 0.25
  2. 0.90
  3. 0.2025

6.

c

Question 8.7

7. A random sample of two Americans is selected. The probability that neither will have type O blood is __________.

7.

0.3025

Question 8.8

8.Figure 8.7 (page 347) shows the 36 possible outcomes for rolling two dice. These outcomes are equally likely. A “soft 4” is a roll of 1 on one die and 3 on the other. The probability of rolling a soft 4 is _________.

8.

Question 8.9

9. A discrete probability model has

  1. only two outcomes.
  2. equally likely outcomes.
  3. a countable number of outcomes.

9.

c

Question 8.10

10. According to Benford’s law, the most likely first (leftmost) digit of a number from financial data is _________.

10.

1

Question 8.11

11. In a table of random digits such as Table 7.1 (page 298), each digit is equally likely to be any of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. What is the probability that a digit in the table is a 0?

  1. 1/9
  2. 1/10
  3. 9/10

11.

b

Question 8.12

12. In a table of random digits such as Table 7.1 (page 298), each digit is equally likely to be any of 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. The probability that a digit in the table is 7 or greater is ___________.

12.

0.3

Question 8.13

13. Toward the end of a game of Scrabble, you hold five tiles with the letters A, E, P, R, and S. In how many ways can you arrange these five letters (whether or not they form actual words)?

  1. 5

13.

b

Question 8.14

14. Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose three of these four letters and arrange them in order in ___________ different ways, assuming that you are not trying to form actual words.

14.

24

Question 8.15

15. A 52-card deck contains 13 cards from each of the four suits: clubs , diamonds , hearts , and spades . You deal four cards without replacement from a well- shuffled deck, so that you are equally likely to deal any four cards. What is the probability that all four cards are clubs?

  1. , because of the cards are clubs

15.

b

Question 8.16

16. You deal four cards as in the previous exercise. The probability that you deal no clubs is _________.

16.

Question 8.17

17. Figure 5.19 (page 209) shows that the normal distribution with mean and standard deviation is a good description of the Iowa Test vocabulary scores of seventh-grade students in Gary, Indiana. The probability that a randomly chosen student has a score higher than 8.4 is

  1. 0.68.
  2. 0.32.
  3. 0.16.

17.

c

389

Question 8.18

18.Figure 8.18 (page 372) shows the density curve of a continuous probability model for choosing a number at random between 0 and 1 inclusive. The probability that the number chosen is less than or equal to 0.4 is __________.

18.

0.4

Question 8.19

19. In Figure 8.18 (page 372), the probability that is greater than 0.65 is

  1. 0.65.
  2. 0.35.
  3. 1.

19.

b

Question 8.20

20. The total area under a density curve is _________.

20.

1

Question 8.21

21. Annual returns on the more than 5000 common stocks available to investors vary a lot. In a recent year, the mean return was 8.3% and the standard deviation of returns was 28.5%. The law of large numbers says that

  1. you can get an average return higher than the mean 8.3% by investing in a large number of stocks.
  2. as you invest in more and more stocks chosen at random, your average return on these stocks gets ever closer to 8.3%.
  3. if you invest in a large number of stocks chosen at random, your average return will have approximately a normal distribution.

21.

b

Question 8.22

22.Figure 8.18 (page 372) shows the density curve of a continuous probability model for choosing a number at random between 0 and 1. The mean of this model is

  1. 0.5 because the curve is symmetric.
  2. 1 because there is area 1 under the curve.
  3. impossible to figure out at this point—this requires advanced mathematics.

22.

a

Question 8.23

23. According to the law of large numbers, as the random phenomenon is repeated a large number of times, gets closer and closer to _______.

23.

the population mean

Question 8.24

24. The expected value is the _________ value.

  1. median
  2. mean
  3. mode

24.

b

Question 8.25

25. The mean payoff of a chance of winning $500 (with a chance of winning $0) is __________.

25.

$50

Question 8.26

26. The density curve of a continuous probability model would balance on the ____________.

  1. mode
  2. median
  3. mean

26.

c

Question 8.27

27. Self Check 14 (page 377) gave a probability model for the number of employees of a small business who call in sick each day. Given , determine the standard deviation.

27.

Question 8.28

28. If , , and , the standard deviation of the sampling distribution of is __________.

28.

2

Question 8.29

29. Scores on the SAT Reasoning Mathematics college entrance test for the class of 2010 were roughly normal, with mean 516 and standard deviation 116. You take an SRS of 100 students and average their SAT scores. If you do this many times, the mean of the average scores that you get from all those samples would be ____________.

29.

516

Question 8.30

30. Referring to Skills Check 29, the standard deviation of the average scores that you get from all those samples would be ____________.

30.

11.6

Question 8.31

31. The number of hours that a light bulb burns before failing varies from bulb to bulb. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that

  1. as we look at more and more bulbs, their average burnout times get ever closer to the mean for all bulbs of this type.
  2. the average burnout times of a large number of bulbs have a distribution of the same shape (strongly skewed) as the distribution for individual bulbs.
  3. the average burnout times of a large number of bulbs have a distribution that is close to normal.

31.

c