PBHL-B300 Homework #3

1. If you flip a fair coin 5 times, what is the probability of:

• Getting all heads?
• Getting all tails?
• Getting at least one head?

2. According to a 2017 Census Bureau survey, 12.6% of Americans are receiving Food Stamp assistance from the government, and 10.5% of Americans have no health insurance. Further, 7.7% of Americans fall into both categories. Using these rates, answer the following:

• Are receiving Food Stamps and having no health insurance disjoint events?
• Explain What percent of Americans are receiving Food Stamps, but have health insurance?
• What percent of Americans are receiving Food Stamps or have no health insurance?
• What percent of Americans are not receiving Food Stamps and have health insurance?
• Is the event of some American receiving Food Stamps independent of the event of not having health insurance?

3. A Gallup survey asks 1,500 Americans about their views regarding Legalization of Marijuana. The table below shows the proportions of responses by political ideology and whether they Favor or Oppose legalizing marijuana:

Favor Legalization	Oppose Legalization	Total
	Conservatives	0.179	0.191	0.374
Political	Moderates	0.278	0.095	0.376
Ideology	Liberals	0.208	0.041	0.251
	Total	0.664	0.327	1.000

1. Are favoring legalization and being a liberal mutually exclusive?
2. What is the probability that a randomly chosen respondent favors legalization or is a liberal?
3. What is the probability that a randomly chosen respondent favors legalization given that he/she is a liberal?
4. What is the probability that a randomly chosen respondent favors legalization given that he/she is a conservative?
5. Is whether or not a respondent favors legalization independent of their political ideology? Explain your answer.
6. What is the probability that a randomly chosen respondent is a moderate given that he/she favors legalization?

4. In the 2016 presidential election Donald Trump received 46.4% of the popular vote. According to exit polls, of those who voted for Trump 19.9% had a high school education or less, while 17.2% of those who voted against Trump had a high school education or less. Suppose we randomly select a respondent from the exit poll and found that he/she has a high school education or less. What is the probability that this respondent voted for Trump?

5. Delta Airlines latest baggage fees for checked luggage are as follows: $30 for the first checked bag, $40 for the second checked bag, and $150 for the third checked bag. Suppose 53% of all Delta passengers have no checked luggage, 33% have one piece of checked luggage, 12% have two pieces, and 2% have three pieces. We also suppose a negligible percent of passengers check more than three bags.

1. Build a probability model for 0, 1, 2, and 3 checked bags and use this to compute the average baggage revenue per passenger.
2. About how much baggage revenue should Delta expect for a flight of 200 passengers?

6. In all marathons run in the USA during 2010, the average (mean) time for men was 4:27 hours (or 267 minutes) with a standard deviation of 1:01 hours (61 minutes). For women running marathons, the average was 4:54 hours (294 minutes) with a standard deviation of 1:02 hours (62 minutes). Suppose the distributions for marathon times are approximately normal for both men and women. John ran the marathon in 5:06 hours (306 minutes), while his wife Mary finished the marathon in 5:09 hours (309 minutes). Obviously John finished the marathon faster than Mary, but they are curious about how each of them performed according to their genders. Remember: a better performance corresponds to a faster (shorter) finish time.

1. Write down the short-hand for the two normal distributions, for men and for women.
2. What are the Z-scores for John's and Mary's finishing times according to their genders? What do these Z-scores tell you when comparing them?
3. Did John or Mary rank better within their own gender?
4. What percent of male marathon runners did John finish faster than?
5. What percent of female marathon runners did Mary finish faster than?
6. If the distributions of finishing times are not nearly normal, would your answers to (b)-(e) be different?
7. According to the above normal distribution for male marathon runners, what would be the cutoff time for the fastest 5% of the men? (that is, those who took the 5% shortest time)
8. According to the above normal distribution for female marathon runners, what would be the cutoff time for the slowest 10% of the women?

7. The average daily high temperature in July in Indianapolis is 85F, with a standard deviation of 6F. Suppose that July temperatures in Indianapolis closely follow a normal distribution.

1. What is the probability of observing a 90F temperature or higher in Indianapolis during a randomly chosen day in July?
2. How cool are the coolest 10% of the days (days with the lowest average high temperature) during July in Indianapolis?