Exam 5: Discrete Random Variables

A pharmaceutical company has determined that if a new cholesterol-reducing drug is manufactured (introduced to the market),the following probability distribution will describe this drug's contribution to the company's profits during the next six months. Profit Contribution Probability of Profit Contribution -\ 30,000 .20 \ 50,000 .50 \ 200,000 .30 The company management has decided to market this product if the expected contribution to profit for the next six months is more than $90,000.Based on the information given above,should the company begin manufacturing the new drug? Explain your answer.

A fair die is rolled 10 times.What is the average number of even number outcomes?

If the population size is at least 20 times larger than the sample size,a hypergeometric distribution can be approximated by the binomial distribution.

The Securities and Exchange Commission has determined that the number of companies listed on the NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month.Find the probability that more than 1 bankruptcy occurs next month.

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number).

Historical data for a local steel manufacturing company show that the average number of defects per standard sheet of steel is 2.In addition,the number of defects per unit is distributed according to a Poisson distribution.What is the probability that there will be a total of 7 defects on four standard sheets of steel?

The variable "employment status," which can take either the value 1 for "employed" and 0 for "unemployed," is an example of a _____________ random variable.

If p = .1 and n = 5,then the corresponding binomial distribution is ____________.

Suppose you randomly select 3 DVDs from a production run of 10.Of the 10 DVDs,9 are expected to last a minimum of 3 years.What is the standard deviation of the random variable x?

The distribution whose mean is equal to its variance is the _________ distribution.

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

Using the following probability distribution table of the random variable x,what is the probability of x = 3? () 0 5/15 1 4/15 2 1/15 3

Suppose you randomly select 3 DVDs from a production run of 10.Of the 10 DVDs,9 are expected to last a minimum of 3 years.What values of x are within two standard deviations of the mean?

According to data from the state blood program,40 percent of all individuals have group A blood.If six individuals give blood,find the probability that none of the individuals has group A blood.

For a binomial process,the probability of success is 40 percent and the number of trials is 5.Find the standard deviation.

The requirement that the probability of success remains constant from trial to trial is a property of the _______________ distribution.

If the number of surface nonconformities on a specific size of metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 defects is given most likely by the _________________ distribution.

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.Determine the expected number of customer arrivals for a five-minute period.

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.