Exam 5: Discrete Probability Distributions

SCENARIO 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Scenario 5-8,if you decide to choose Design A for half of the production lines and Design B for the other half,what is the coefficient of variation of your investment?

SCENARIO 5-10 An accounting firm in a college town usually recruits employees from two of the universities in town.This year,there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Scenario 5-10,what is the probability that none of the new employees will be from University A?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The variance of the number of power outages is _____.

The expected return of a two-asset portfolio is equal to the product of the weight assigned to the first asset and the expected return of the first asset plus the product of the weight assigned to the second asset and the expected return of the second asset.

SCENARIO 5-5 From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed. -Referring to Scenario 5-5,what is the probability out of the 8 new cars it just received that,when each is tested,no more than 2 of the cars have defective radios?

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7,what is the standard deviation of the value gain for the house in neighborhood B?

SCENARIO 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers.In a recent year,the hotel chain had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Scenario 5-9,what is the probability that in the next 1,000 customers,the hotel chain will have more than five but less than eight mishandled bags?

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7,if you can invest 70% of your money on the house in neighborhood A and the remaining on the house in neighborhood B,what is the portfolio expected return of your investment?

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7,what is the covariance of the two houses?

A stock analyst was provided with a list of 25 stocks.He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days.The prices of only 5 stocks would rise by more than 20% after 30 days.If he randomly selected 3 stocks from the list,he would use what type of probability distribution to compute the probability that all the chosen stocks would appreciate more than 20% after 30 days?

A financial analyst is presented with information on the past records of 60 start-up companies and told that in fact only 3 of them have managed to become highly successful.He selected 3 companies from this group as the candidates for success.To analyze his ability to spot the companies that will eventually become highly successful,he will use what type of probability distribution?

The expected return of the sum of two investments will be equal to the sum of the expected returns of the two investments plus twice the covariance between the investments.

SCENARIO 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete,so it is reasonable to believe that their relative successes would be independent). -Referring to Scenario 5-2,the probability that all 3 businesses succeed is _____.

The number of males selected in a sample of 5 students taken without replacement from a class of 9 females and 18 males has a binomial distribution.

SCENARIO 5-5 From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed. -Referring to Scenario 5-5,what is the probability out of the 8 new cars it just received that,when each is tested,exactly two of the cars have non-defective radios?

SCENARIO 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Scenario 5-8,if your investment preference is to maximize your expected profit and not worry at all about the risk that you must take,will you choose a production mix that will consist of 10%,30%,50%,70%,or 90% of your production lines for Design A and the remaining for Design B?

SCENARIO 5-13 Bell Computers manufactures personal computers at two plants,one in Arkansas and one in Utah.The Arkansas plant has 50 employees;the Utah one has 40 employees.A random sample of 12 employees was selected to complete a job satisfaction questionnaire -Using Scenario 5-13,What is the probability fewer than five employees completing the questionnaire are from the Utah plant?

The diameters of 10 randomly selected bolts have a binomial distribution.

SCENARIO 5-3 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network. -Referring to Scenario 5-3,the probability of no retransmissions is _____.

A national trend predicts that women will account for half of all business travelers in the next 3 years.To attract these women business travelers,hotels are providing more amenities that women particularly like.A recent survey of American hotels found that 70% offer hairdryers in the bathrooms.Consider a random and independent sample of 20 hotels.Find the probability that at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.