4.1 Homework (modified r. bloom)  (Page 4/6)

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.

• 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.

• F

  Find the probability that no more than 6 students of Shotokan Karate are picked.

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.

Refer to the previous problem . Suppose that 100 people with tax returns over $25,000 are randomly picked. We are interested in the number of people audited in 1 year. One way to solve this problem is by using the Binomial Distribution. Since $n$ is large and $p$ is small, another discrete distribution could be used to solve the following problems. Solve the following questions (d-f) using that distribution.

• D

  How many are expected to be audited?

• E

  Find the probability that no one was audited.

• F

  Find the probability that more than 2 were audited.

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that 10 people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and 8 who are not. We are interested in the number on the committee who are not technically proficient.

• D

  How many instructors do you expect on the committee who are not technically proficient?

• E

  Find the probability that at least 5 on the committee are not technically proficient.

• F

  Find the probability that at most 3 on the committee are not technically proficient.