5.14 Homework  (Page 4/7)

The average number of children a Spanish woman has in her lifetime is 1.47. Suppose that one Spanish woman is randomly chosen. ( http://www.typicallyspanish.com/news/publish/article_4897.shtml ).

• d Find the probability that she has no children.
• e Find the probability that she has fewer children than the Spanish average.
• f Find the probability that she has more children than the Spanish average .

Fertile (female) cats produce an average of 3 litters per year. (Source: The Humane Society of the United States) . Suppose that one fertile, female cat is randomly chosen. In one year, find the probability she produces:

• d No litters.
• e At least 2 litters.
• f Exactly 3 litters.

A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be 28%. We are interested in the number of dealerships she must call.

• d On average, how many dealerships would we expect her to have to call until she finds one that has the car?
• e Find the probability that she must call at most 4 dealerships.
• f Find the probability that she must call 3 or 4 dealerships.

Suppose that the probability that an adult in America will watch the Super Bowl is 40%. Each person is considered independent. We are interested in the number of adults in America we must survey until we find one who will watch the Super Bowl.

• d How many adults in America do you expect to survey until you find one who will watch the Super Bowl?
• e Find the probability that you must ask 7 people.
• f Find the probability that you must ask 3 or 4 people.

A group of Martial Arts students is planning on participating in an upcoming demonstration. 6 are students of Tae Kwon Do; 7 are students of Shotokan Karate. Suppose that 8 students are randomly picked to be in the first demonstration. We are interested in the number of Shotokan Karate students in that first demonstration. Hint: Use the Hypergeometric distribution. Look in the Formulas section of 4: Discrete Distributions and in the Appendix Formulas.

• d How many Shotokan Karate students do we expect to be in that first demonstration?
• e Find the probability that 4 students of Shotokan Karate are picked for the first demonstration.
• f Suppose that we are interested in the Tae Kwan Do students that are picked for the first demonstration. Find the probability that all 6 students of Tae Kwan Do are picked for the first demonstration.

The chance of a IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 20 year period. Assume each year is independent.

• d How many audits are expected in a 20 year period?
• e Find the probability that a person is not audited at all.
• f Find the probability that a person is audited more than twice.