Exam 16: Probability Models

A multiple choice test has 9 questions each of which has 4 possible answers,only one of which is correct.If Judy,who forgot to study for the test,guesses on all questions,what is the probability that she will answer exactly 3 questions correctly?

A tennis player makes a successful first serve 65% of the time.Assume that each serve is independent of the others.If she serves 3 times,what is the probability that she does not make all of her first serves?

A tennis player makes a successful first serve 64% of the time.If she serves 6 times,what is the probability that she gets no more than 3 first serves in? Assume that each serve is independent of the others.

An archer is able to hit the bull's-eye 48% of the time.If she shoots 8 arrows,what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

Suppose the probability of a major earthquake on a given day is 1 out of 10,000.What's the expected number of earthquakes in the next 2,000 days?

A company finds that 74% of applicants for a job do not have the required qualifications.How many applications should they expect to read before finding a suitably qualified applicant?

In one city,police estimate that 78% of drivers wear their seat belts.They set up a safety roadblock and they stop drivers to check for seat belt use.If 160 drivers are stopped,what's the probability they find at least 30 not wearing their seat belts?

A tennis player makes a successful first serve 70% of the time.If she serves 80 times,is it appropriate to use a normal model to approximate the distribution of the number of good first serves? Assume that each serve is independent of the others.

A basketball player has made 65% of his foul shots during the season.Assuming the shots are independent,find the probability that in tonight's game he makes his first basket on one of his first 4 shots.

Suppose that 2.4% of people are left handed.If 30 people are selected at random,what is the standard deviation of the number of right-handers in the group?

A tennis player usually makes a successful first serve 69% of the time.She buys a new racket hoping that it will improve her success rate.When she first tests her new racket she makes 4 first serves in a row.Is this evidence that with the new racket her success rate has improved? In other words,is a streak like this unusual for her? Explain.

Police estimate that 65% of drivers wear their seat belts.If they stop 4 drivers at random,what's the probability that none of them are wearing their seat belts?

A tennis player makes a successful first serve 65% of the time.If she serves 90 times in a match,what's the probability that she makes no more than 50 first serves? Assume that each serve is independent of the others.

The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with a mean of 2.8.Find the probability that in a randomly selected year,the number of lightning strikes is 2.

On one tropical island,hurricanes occur with a mean of 2.26 per year.Assuming that the number of hurricanes can be modeled by a Poisson distribution,find the probability that there will be no hurricanes next year.

Police estimate that in one city 83% of drivers wear their seat belts.They set up a safety roadblock,stopping cars to check for seat belt use.If they stop 30 cars during the first hour,what is the standard deviation of the number of drivers expected to be wearing their seat belts?

At one college,66% of students have credit cards.A credit card company,looking for new customers,sets up a booth at the college.If they pick students at random,how many students should they expect to talk to before finding one who does not have a credit card?

A laboratory worker finds that 1.6% of his blood samples test positive for the HIV virus.In a random sample of 130 blood tests,what is the standard deviation of the number that test positive for the HIV virus?

A beginning archer is able to hit the bull's-eye 41% of the time.If she shoots 7 arrows,what is the probability that she gets at most 3 bull's-eyes? Assume each shot is independent of the others.

A multiple choice test has 6 questions each of which has 4 possible answers,only one of which is correct.If Judy,who forgot to study for the test,guesses on all questions,what is the probability that she will answer none of the questions correctly?