Solutions

0.10 + 0.05 = 0.15

1

0.35 + 0.40 + 0.10 = 0.85

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

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

1 – 0.05 = 0.95

X = the number of business majors in the sample.

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

X = the number that reply “yes”

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

5.7

0.4151

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

1,2,…

1.4

0, 1, 2, 3, 4, …

0.0485

0.0214

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

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

No

1. X = the number of pages that advertise footwear
2. 0, 1, 2, 3, ..., 20
3. 3.03
4. 1.5197

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

X = the number of patients calling in claiming to have the flu, who actually have the flu.

X = 0, 1, 2, ...25

0.0165

1. X = the number of video games a Game Stop customer rents
2. 0.12
3. 0.11
4. 0.77

d. 4.43

c

• X = number of questions answered correctly
• X ~ B$\left(\text{32, }\frac{\text{1}}{\text{3}}\right)$
• 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.

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.

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.

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

1. X = the number of matches
2. 0, 1, 2, 3
3. In dollars: −1, 1, 2, 3
4. $\frac{1}{2}$
5. The answer is −0.0787. You lose about eight cents, on average, per game.
6. The house has the advantage.

1. X ~ B(15, 0.281)

   Figure 4.5
2. 1. Mean = μ = np = 15(0.281) = 4.215
   2. Standard Deviation = σ = $\sqrt{npq}$ = $\sqrt{15(0.281)(0.719)}$ = 1.7409
3. 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.

1. X = the number of adults in America who are surveyed until one says they will watch the Super Bowl.
2. X ~ G(0.40)
3. 2.5
4. 0.0187
5. 0.2304

1. X = the number of pages that advertise footwear
2. X takes on the values 0, 1, 2, ..., 20
3. X ~ B(20, $\frac{29}{192}$)
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($\frac{29}{192}$)
8. 0.3881
9. 6.6207 pages

0, 1, 2, and 3

1. X ~ G(0.25)
2. 1. Mean = μ = $\frac{1}{p}$ = $\frac{1}{0.25}$ = 4
   2. Standard Deviation = σ = $\sqrt{\frac{1-p}{p^2}}$ = $\sqrt{\frac{1-\text{0}\text{.25}}{{0.25}^2}}$ ≈ 3.4641
3. P(x = 10) = 0.0188
4. P(x = 20) = 0.0011
5. P(x ≤ 5) = 0.7627

1. X ~ P(5.5); μ = 5.5; $\sigma \text{ = }\sqrt{5.5}$ ≈ 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

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.

1. X = the number of children for a Spanish woman
2. 0, 1, 2, 3,...
3. 0.2299
4. 0.5679
5. 0.4321

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.

1. X = the number of people audited in one year
2. 0, 1, 2, ..., 100
3. 2
4. 0.1353
5. 0.3233

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

d