Exam 5: Discrete Probability Distributions

If n = 10 and $\pi$ = 0.70,then the mean of the binomial distribution is

In a Poisson distribution,the mean and standard deviation are equal.

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 between 1 and 3 inclusive power outages in a year is _____.

SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month.Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. -Referring to Scenario 5-11,what is probability that no security transaction will be conducted in one month?

SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month.Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. -Referring to Scenario 5-11,what is mean number of transactions per month for this subscriber?

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 at least one of the new employees will be from University A?

Whenever $\pi$ = 0.5,the binomial distribution will

The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that exactly 5 bankruptcies occur next month.

In a game called Taxation and Evasion,a player rolls a pair of dice.If on any turn the sum is 7,11,or 12,the player gets audited.Otherwise,she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The variance of the number of times she will be audited is _____.

In a game called Taxation and Evasion,a player rolls a pair of dice.If,on any turn,the sum is 7,11,or 12,the player gets audited.Otherwise,she avoids taxes.Suppose a player takes 5 turns at rolling the dice.The probability that she does not get audited is _____.

What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem? An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims.It is known that the industry proportion for false claims is 3%.The consulting firm has decided to randomly and independently sample 100 of the company's insurance claims.They believe the number of these 100 that are false will yield the information the company desires.

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The mean number of airplanes arriving per minute is 3.The probability that exactly 6 planes arrive in the next minute is 0.05041.

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 variance of the gain in value for the house in neighborhood A?

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students.Ten of the 15 students have no prior competition experience while the others have some degree of experience.What is the probability that none of the members chosen for the team have any competition experience?

SCENARIO 5-1 The probability that a 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 Scenario 5-1,the probability that neither sound an alarm in the presence of smoke is_____.

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 30% of your money on the house in neighborhood A and the remaining on the house in neighborhood B,what is the portfolio risk of your investment?

SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month.Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. -Referring to Scenario 5-11,what is probability that no more than five security transactions will be conducted in one month?

The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that more than 3 bankruptcies occur next month.

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week.Interpret this value.

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 half of the cars have non-defective radios?