Exam 16: Probability Models

On a multiple choice test with 15 questions,each question has four possible answers,one of which is correct.For students who guess at all answers,find the standard deviation of the number of correct answers.

In one city,police estimate that 79% of drivers wear their seat belts.They set up a safety roadblock and they stop drivers to check for seat belt use.If 150 drivers are stopped,is it appropriate to use a normal model to approximate the distribution of the number whose seat belt is not buckled?

A basketball player has made 75% of his foul shots during the season.Assuming the shots are independent,find the expected number of shots until he misses.

A tennis player makes a successful first serve 90% of the time.Assume that each serve is independent of the others.If she serves 10 times,what is the probability that she misses for the first time on her second or fourth serve?

An airline,believing that 6% of passengers fail to show up for flights,overbooks.Suppose a plane will hold 320 passengers and the airline sells 335 seats.What's the probability the airline will not have enough seats and will have to bump someone?

An airline has found that on average,8% of its passengers request vegetarian meals.On a flight with 360 passengers the airline has 35 vegetarian dinners available.What's the probability that it will be short of vegetarian dinners?

Suppose that in one city,79% of cars parked at meters still have time remaining on the meter.How many cars should a meter maid expect to check before finding one at an expired meter?

The probability that a call received by a certain switchboard will be a wrong number is 0.01.Use the Poisson approximation to the binomial distribution to find the probability that among 120 calls received by the switchboard,there are no wrong numbers.

In the town of Blue Valley,7% of female college students suffer from manic-depressive illness.If 170 of the female students are selected at random,what is the mean of the number who suffer from manic-depressive illness?

A computer salesman averages 1.9 sales per week.Use the Poisson distribution to find the probability that in a randomly selected week the number of computers sold is 1.

How likely is it that in a group of 400 people,the majority have blue eyes,given that 22% of the population have blue eyes? Assume that the people are unrelated to each other.

In a certain town,8% of female college students suffer from manic-depressive illness.If 230 of the female students are selected at random,what is the standard deviation of the number who suffer from manic-depressive illness?

Suppose that 74% of tax returns are free of errors.How many returns should an IRS auditor expect to check before finding one with errors?

A tennis player makes a successful first serve 59% of the time.If she serves 29 times,what is the standard deviation of the number of good first serves? Assume that each serve is independent of the others.

Suppose that in a certain population 8% of people are color blind.A researcher selects people at random from this population.What's the probability that the first color blind person will be found among the first 6 people checked?

Suppose that 10% of people are left handed.If 5 people are selected at random,what is the probability that exactly 2 of them are left handed?

A car insurance company has determined that 7% of all drivers were involved in a car accident last year.If 11 drivers are randomly selected,what is the probability that at least 3 were involved in a car accident last year?

In a certain town,5% of college students suffer from manic-depressive illness.If 300 of the students are selected at random and screened,what is the probability that no more than 20 of them suffer from manic-depressive illness?

You roll a die 7 times and need to get at least three 2's to win the game.

Suppose a computer chip manufacturer rejects 4% of the chips produced because they fail presale testing.How many chips should they expect to test before finding a bad one?