Exam 14: Random Variables

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

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?

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.

A company is interviewing applicants for managerial positions.They plan to hire two people.They have already rejected most candidates and are left with a group of 7 applicants of whom 6 are women.Unable to differentiate further between the applicants,they choose two people at random from this group of 7.Let the random variable X be the number of men that are chosen.Find the standard deviation of X.

Suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.If you test 4 chips,what is the probability that all of the chips fail?

The amount of money that Maria earns in a week is a random variable with a mean of $970 and a standard deviation of $25.The amount of money that Elena earns in a week is a random variable with a mean of $860 and a standard deviation of $10.How much more do you expect Maria to earn in a week than Elena? What is the standard deviation of this difference? Assume that Maria's earnings are independent of Elena's earnings.

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

A company realizes that 5% of its pens are defective.In a package of 30 pens,is it likely that more than 6 are defective? Assume that pens in a package are independent of each other.

For students who guess at all answers,find the standard deviation of the number of correct answers.

You have arranged to go camping for two days in March.You believe that the probability that it will rain on the first day is 0.5.If it rains on the first day,the probability that it also rains on the second day is 0.7.If it doesn't rain on the first day,the probability that it rains on the second day is 0.2.Let the random variable X be the number of rainy days during your camping trip.Find the expected value of X.

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?

A couple plans to have children until they get a boy,but they agree that they will not have more than four children even if all are girls.Find the expected number of children they will have.Assume that boys and girls are equally likely.Round your answer to three decimal places.

An insurance policy costs $140 per year,and will pay policyholders $15,000 if they suffer a major injury (resulting in hospitalization)or $7000 if they suffer a minor injury (resulting in lost time from work).The company estimates that each year 1 in every 2200 policyholders will have a major injury and 1 in every 400 a minor injury.What is the company's expected profit on this policy?

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 company selling vegetable seeds in packets of 40 estimates that the mean number of seeds that will actually grow is 35.7 with a standard deviation of 1.9 seeds.If a customer buys 5 different seed packets,what are the expected value and standard deviation of the number of bad seeds? Assume that packets are independent of each other.

The probabilities that a batch of 4 computers will contain 0,1,2,3,and 4 defective computers are 0.4096,0.4096,0.1536,0.0256,and 0.0016,respectively.Find the expected number of defective computers in a batch of 4.

The accompanying table describes the probability distribution for the number of adults in a certain town (among 4 randomly selected adults)who have a degree from a post-secondary institute.Find the standard deviation for the probability distribution. () 0 0.0256 1 0.1536 2 0.3456 3 0.3456 4 0.1296

Given independent random variables with means and standard deviations as shown,find the mean and standard deviation of the variable 2X. Mean SD 40 5 70 8

0 1 2 (=) 0.5 0.2 0.3

Bill claims that he has a coin which is biased and which comes up heads more than tails.His claim is based on a trial in which he flipped the coin 200 times and got 110 heads.If the coin were actually fair,what would be the probability of getting 110 or more heads?