Exam 16: Probability Models

Suppose that in a certain population 45% of people have type O blood.A researcher selects people at random from this population.What is the probability that there is a person with type O blood among the first 6 people checked?

A basketball player has made 78% of his foul shots during the season.Assuming the shots are independent,find the probability that in tonight's game he misses for the first time on his 5th attempt?

People with O-negative blood are called "universal donors" because O-negative blood can be given to anyone else regardless of the recipient's blood type.About 6% of people have type O-negative blood.A clinic is running a blood drive.If at least 220 O-negative donors give blood,the clinic will have sufficient O-negative blood for the coming month.If 4000 donors come to the blood drive,what's the probability that the clinic will not have sufficient O-negative donors?

A laboratory worker finds that 1.4% of his blood samples tested positive for the HIV virus.How many blood samples should he expect to test before finding one which tests positive for the HIV virus?

The number of calls received by a mountain search and rescue team in a day has a Poisson distribution with a mean of 0.71.Find the probability that on a randomly selected day,they will receive fewer than two calls.

A tennis player makes a successful first serve 57% of the time.If she serves 6 times,what is the probability that she gets all her first serves in? Assume that each serve is independent of the others.

Suppose the probability of contracting a certain disease is p = 0.0004 for a new case in a given year.What's the expected number of new cases in a year in a town where 4,000 people do not currently have the disease?

A laboratory worker finds that 1.8% of his blood samples test positive for the HIV virus.If 270 blood samples are selected at random,is it appropriate to use a normal model to approximate the distribution of the number that test positive for the HIV virus?

Suppose that 14% of students at one college have high blood pressure.If you keep picking students at random from this college,how many students do you expect to test before finding one with high blood pressure?

A company manufactures batteries in batches of 23 and there is a 3% rate of defects.Find the standard deviation of the number of defects per batch.

A company manufactures batteries in batches of 10 and there is a 3% rate of defects.Find the mean number of defects per batch.

Suppose that in a certain population 46% of people have type O blood.A researcher selects people at random from this population.What's the probability they won't find a person with type O blood among the first 4 people checked?

A tennis player makes a successful first serve 54% of the time.If she serves 5 times,what is the probability that she gets exactly 3 first serves in? Assume that each serve is independent of the others.

A sailing school offers sailing lessons on Sundays for adults.It has 20 life jackets available in the small size and 25 in the large size.It has found that 55% of adults need the large size and the remainder the small size.If 40 adults show up for lessons one Sunday morning,what is the probability that the school will run out of the small life jackets and that someone needing the small size will have to wear a large life jacket?