Exam 5: Some Important Discrete Probability Distributions

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -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 analyse his ability to identify the companies that will eventually become highly successful,he will use what type of probability distribution?

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5-8,what is the probability that in the next 1,000 customers,the airline will have more than ten mishandled bags?

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5-8,what is the probability that in the next 1,000 customers,the airline will have less than two or more than eight mishandled bags?

Instruction 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent). -Referring to Instruction 5-2,the probability that at least 1 business succeeds is ________.

Instruction 5-6 From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed. -Referring to Instruction 5-6,what is the probability out of the 8 new cars it just received that,when each is tested,at least half of the cars have defective radios?

Instruction 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 double satellite media. X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 -Referring to Instruction 5-3,the standard deviation of the number of retransmissions is ________.

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be at least 3 power outages in a year is ________.

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.

Instruction 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent). -Referring to Instruction 5-2,the probability that exactly 1 business succeeds is ________.

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5-8,what is the probability that in the next 1,000 customers,the airline will have no more than two or at least eight mishandled bags?

Instruction 5-5 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Instruction 5-5,what is the standard deviation of the value gain for the house in neighbourhood B?

Suppose that past history shows that 60% of university students prefer Brand C cola.A sample of 5 students is to be selected.The probability that at least 1 prefers Brand C is ________.

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -A major retailer in Australia wishes to form a team of 16 executives from different departments within the company.Suppose the company has a total of 60 executives,and 20 of these are from the marketing department.If the members of the team are to be selected at random,what type of probability distribution can be used to figure out the probability that the team will contain four executives from the marketing department?

Instruction 5-7 The quality control manager of Marilyn's Biscuits is inspecting a batch of chocolate chip biscuits.When the production process is in control,the average number of chocolate chip parts per biscuit is 6.0. -Referring to Instruction 5-7,what is the probability that any particular biscuit being inspected has between 5.0 and 8.0 inclusive chip parts?

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.

Instruction 5-1 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently. -Referring to Instruction 5-1,the probability that at least one sounds an alarm in the presence of smoke is ________.

If X has a binomial distribution with n = 4 and p = 0.3,then P(X = 1)= ________.

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have five such alarms in your home and they operate independently.Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5-8,what is the probability that in the next 1,000 customers,the airline will have no more than four mishandled bags?

Whenever p = 0.1 and n is small,the binomial distribution will be