Exam 16: Probability Models

An archer is able to hit the bull's eye 76% of the time.If she shoots 160 arrows in a competition,what's the probability that she gets at least 130 bull's-eyes? Assume that shots are independent of each other.

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.What is the probability that the seventh chip you test is the first bad one you find?

The probability that a car will have a flat tire while driving through a certain tunnel is 0.00005.Use the Poisson approximation to the binomial distribution to find the probability that among 14,000 cars passing through this tunnel,exactly two will have a flat tire.

A basketball player has made 70% of his foul shots during the season.If he shoots 6 foul shots in tonight's game,what is the probability that he doesn't make all of the shots?

Suppose the probability of contracting a certain disease is p = 0.0004 for a new case in a given year.Use the Poisson model to approximate the probability that in a town where 1,000 uninfected people there will be at least one new case of the disease next year.

Sunita's job is to provide technical support to computer users.Suppose the arrival of calls can be modeled by a Poisson distribution with a mean of 4.9 calls per hour.What's the probability that in the next 30 minutes there will be 2 or more calls?

An archer is able to hit the bull's-eye 71% of the time.If she shoots 10 arrows,what is the probability that her first bull's-eye comes on the 5th arrow? Assume each shot is independent of the others.

Sunita's job is to provide technical support to computer users.Suppose the arrival of calls can be modeled by a Poisson distribution with a mean of 5.6 calls per hour.What's the probability that in the next 10 minutes there will be no calls?

We record the blood types (O,A,B,or AB)found in a group of 100 people.Assume that the people are unrelated to each other.

A basketball player usually makes 58% of his free shots.Tonight he made 10 shots in a row.Is this evidence that he is on a winning streak? That is,is this streak so unusual that it means the probability he makes a shot must have changed? Explain.

Police estimate that in one city 48% of drivers wear their seat belts.They set up a safety roadblock,stopping cars to check for seat belt use.If they stop 70 cars during the first hour,what is the mean of the number of drivers expected to be wearing their seat belts?

A multiple choice test consists of 60 questions.Each question has 4 possible answers only one of which is correct.A student answers 26 questions correctly.Is that enough to convince you that he is not merely guessing? Explain.

The rate of defects among CD players of a certain brand is 1.1%.Use the Poisson approximation to the binomial distribution to find the probability that among 270 such CD players received by a store,there is at most one defective.

A pool of possible jurors consists of 15 men and 18 women.A jury of 12 is picked at random from this group.What is the probability that the jury contains all women?

An archer is able to hit the bull's eye 74% of the time.If she shoots 130 arrows in a competition,is it appropriate to use a normal model to approximate the distribution of the number of bull's-eyes? Assume that shots are independent of each other.

The probability that a call received by a certain switchboard will be a wrong number is 0.02.Use the Poisson approximation to the binomial distribution to find the probability that among 140 calls received by the switchboard,there are at least two wrong numbers.

Police estimate that 25% of drivers drive without their seat belts.If they stop 4 drivers at random,find the probability that all of them are wearing their seat belts.

Suppose that 11% of people are left handed.If 26 people are selected at random,what is the mean of the number of right-handers in the group?

The probability that a radish seed will germinate is 0.7.A gardener plants seeds in batches of 4.Find the standard deviation of the number of seeds germinating in each batch.

A laboratory worker finds that 1.6% of his blood samples test positive for the HIV virus.In a random sample of 140 blood tests,what is the mean number that test positive for the HIV virus?