# Solutions

1.
xP(x)
00.12
10.18
20.30
30.15
40.10
50.10
60.05
Table 4.6
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.
xP(x)
00.03
10.04
20.08
30.85
Table 4.7
13.

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

15.
xP(x)
00.05
10.05
20.10
30.20
40.25
50.35
Table 4.8
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.
1. X = the number of pages that advertise footwear
2. 0, 1, 2, 3, ..., 20
3. 3.03
4. 1.5197
50.
1. X = the number of Patriots picked
2. 0, 1, 2, 3, 4
3. 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.
1. X = the number of DVDs a Video to Go customer rents
2. 0.12
3. 0.11
4. 0.77
59.

d. 4.43

61.

c

63.
• X = number of questions answered correctly
• X ~ B
• 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.
1. X = the number of college and universities that offer online offerings.
2. 0, 1, 2, …, 13
3. X ~ B(13, 0.96)
4. 12.48
5. 0.0135
6. P(x = 12) = 0.3186 P(x = 13) = 0.5882 More likely to get 13.
67.
1. X = the number of fencers who do not use the foil as their main weapon
2. 0, 1, 2, 3,... 25
3. X ~ B(25,0.40)
4. 10
5. 0.0442
6. The probability that all 25 not use the foil is almost zero. Therefore, it would be very surprising.
69.
1. X = the number of audits in a 20-year period
2. 0, 1, 2, …, 20
3. X ~ B(20, 0.02)
4. 0.4
5. 0.6676
6. 0.0071
71.
1. X = the number of matches
2. 0, 1, 2, 3
3. In dollars: −1, 1, 2, 3
4. $1 2 1 2$
5. The answer is −0.0787. You lose about eight cents, on average, per game.
6. The house has the advantage.
73.
1. X ~ B(15, 0.281)
Figure 4.4
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
2. 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.
1. X = the number of adults in America who are surveyed until one says he or she will watch the Super Bowl.
2. X ~ G(0.40)
3. 2.5
4. 0.0187
5. 0.2304
77.

1. X = the number of pages that advertise footwear
2. X takes on the values 0, 1, 2, ..., 20
3. X ~ B(20, $2919229192$)
4. 3.02
5. No
6. 0.9997
7. X = the number of pages we must survey until we find one that advertises footwear. X ~ G($2919229192$)
8. 0.3881
9. 6.6207 pages
79.

0, 1, 2, and 3

81.
1. X ~ G(0.25)
1. Mean = μ = $1 p 1 p$ = $1 0.25 1 0.25$ = 4
2. Standard Deviation = σ = $1−p p 2 1−p p 2$ = $1−0.25 0.25 2 1−0.25 0.25 2$ ≈ 3.4641
2. P(x = 10) = 0.0188
3. P(x = 20) = 0.0011
4. P(x ≤ 5) = 0.7627
82.
1. X ~ P(5.5); μ = 5.5; ≈ 2.3452
2. P(x ≤ 6) ≈ 0.6860
3. There is a 15.7% probability that the law staff will receive more calls than they can handle.
4. P(x > 8) = 1 – P(x ≤ 8) ≈ 1 – 0.8944 = 0.1056
84.

Let X = the number of defective bulbs in a string.

Using the Poisson distribution:

• μ = np = 100(0.03) = 3
• X ~ P(3)
• P(x ≤ 4) ≈ 0.8153

Using the binomial distribution:

• X ~ B(100, 0.03)
• P(x ≤ 4) = 0.8179

The Poisson approximation is very good—the difference between the probabilities is only 0.0026.

86.
1. X = the number of children for a Spanish woman
2. 0, 1, 2, 3,...
3. 0.2299
4. 0.5679
5. 0.4321
88.
1. X = the number of fortune cookies that have an extra fortune
2. 0, 1, 2, 3,... 144
3. 4.32
4. 0.0124 or 0.0133
5. 0.6300 or 0.6264
6. As n gets larger, the probabilities get closer together.
90.
1. X = the number of people audited in one year
2. 0, 1, 2, ..., 100
3. 2
4. 0.1353
5. 0.3233
92.
1. X = the number of shell pieces in one cake
2. 0, 1, 2, 3,...
3. 1.5
4. 0.2231
5. 0.0001
6. Yes
94.

d