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4.13: Solutions

Last updated

Mar 17, 2025
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- 4.12: References
- 5: Continuous Random Variables

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Table $\PageIndex{1}$
$x$	$P(x)$
0	0.12
1	0.18
2	0.30
3	0.15
4	0.10
5	0.10
6	0.05

3. 0.10 + 0.05 = 0.15

5. 1

7. 0.35 + 0.40 + 0.10 = 0.85

9. 1(0.15) + 2(0.35) + 3(0.40) + 4(0.10) = 0.15 + 0.70 + 1.20 + 0.40 = 2.45

11.

Table $\PageIndex{2}$
$x$	$P(x)$
0	0.03
1	0.04
2	0.08
3	0.85

13. Let $X =$ the number of events Javier volunteers for each month.

15.

Table $\PageIndex{3}$
$x$	$P(x)$
0	0.05
1	0.05
2	0.10
3	0.20
4	0.25
5	0.35

17. 1 – 0.05 = 0.95

18. $X =$ the number of business majors in the sample.

19. 2, 3, 4, 5, 6, 7, 8, 9

20. $X =$ the number that reply “yes”

22. 0, 1, 2, 3, 4, 5, 6, 7, 8

24. 5.7

26. 0.4151

28. $X =$ the number of freshmen selected from the study until one replied "yes" that same-sex couples should have the right to legal marital status.

30. 1,2,…

32. 1.4

35. 0, 1, 2, 3, 4, …

37. 0.0485

39. 0.0214

41. $X =$ the number of U.S. teens who die from motor vehicle injuries per day.

43. 0, 1, 2, 3, 4, ...

45. No

48.

X = the number of pages that advertise footwear
0, 1, 2, 3, ..., 20
3.03
1.5197

50.

X = the number of Patriots picked
0, 1, 2, 3, 4
Without replacement

53. $X =$ the number of patients calling in claiming to have the flu, who actually have the flu. X = 0, 1, 2, ...25

55. 0.0165

57.

X = the number of DVDs a Video to Go customer rents
0.12
0.11
0.77

59. 4.43

61. c

63.

X = number of questions answered correctly
X ~ B(32, 13)(32, 13)
We are interested in MORE THAN 75% of 32 questions correct. 75% of 32 is 24. We want to find P(x > 24). The event "more than 24" is the complement of "less than or equal to 24."
P(x > 24) = 0
The probability of getting more than 75% of the 32 questions correct when randomly guessing is very small and practically zero.

65.

X = the number of college and universities that offer online offerings.
0, 1, 2, …, 13
X ~ B(13, 0.96)
12.48
0.0135
P(x = 12) = 0.3186 P(x = 13) = 0.5882 More likely to get 13.

67.

X = the number of fencers who do not use the foil as their main weapon
0, 1, 2, 3,... 25
X ~ B(25,0.40)
10
0.0442
The probability that all 25 not use the foil is almost zero. Therefore, it would be very surprising.

69.

X = the number of audits in a 20-year period
0, 1, 2, …, 20
X ~ B(20, 0.02)
0.4
0.6676
0.0071

71.

X = the number of matches
0, 1, 2, 3
In dollars: −1, 1, 2, 3
1212
The answer is −0.0787. You lose about eight cents, on average, per game.
The house has the advantage.

73.

X ~ B(15, 0.281)
1. Mean = μ = np = 15(0.281) = 4.215
2. Standard Deviation = σ = npq−−−√𝑛𝑝𝑞 = 15(0.281)(0.719)−−−−−−−−−−−−−√15(0.281)(0.719) = 1.7409
P(x > 5)=1 – 0.7754 = 0.2246
P(x = 3) = 0.1927
P(x = 4) = 0.2259
It is more likely that four people are literate that three people are.

75.

X = the number of adults in America who are surveyed until one says he or she will watch the Super Bowl.
X ~ G(0.40)
2.5
0.0187
0.2304

77.

X = the number of pages that advertise footwear
X takes on the values 0, 1, 2, ..., 20
X ~ B(20, 2919229192)
3.02
No
0.9997
X = the number of pages we must survey until we find one that advertises footwear. X ~ G(2919229192)
0.3881
6.6207 pages

79. 0, 1, 2, and 3

81.

X ~ G(0.25)
1. Mean = μ = 1p1𝑝 = 10.2510.25 = 4
2. Standard Deviation = σ = 1−pp2−−−√1−𝑝𝑝2 = 1−0.250.252−−−−−√1−0.250.252 ≈ 3.4641
P(x = 10) = 0.0188
P(x = 20) = 0.0011
P(x ≤ 5) = 0.7627

82.

X ~ P(5.5); μ = 5.5; σ = 5.5−−−√𝜎 = 5.5 ≈ 2.3452
P(x ≤ 6) ≈ 0.6860
There is a 15.7% probability that the law staff will receive more calls than they can handle.
P(x > 8) = 1 – P(x ≤ 8) ≈ 1 – 0.8944 = 0.1056