Exam 5: Some Important Discrete Probability Distributions

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 all 3 businesses fail 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 at least one 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,if you can invest 10% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Instruction 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 -The standard deviation of a discrete random variable is the square root of the ________.

Instruction 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth. X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 -Referring to Instruction 5-4,the variance of the number of accidents is ________.

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 expected value gain if you invest in both houses?

The Poisson distribution can be used to model a continuous random variable.

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 and more than eight mishandled bags?

Instruction 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year's rat orders be,assuming this distribution does not change?

A multiple-choice test has 30 questions.There are 4 choices for each question.A student who has not studied for the test decides to answer all questions randomly.What type of probability distribution can be used to figure out his chance of getting at least 20 questions right?

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,if you can invest 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

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 fewer than eight mishandled bags?

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 gets audited at least once is ________.

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 at least 6.0 chip parts?

Numerical variables are classified as either discrete or continuous.

Instruction 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -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.

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 4.0 chip parts?

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,no more than half of the cars have defective radios?

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 five but less than eight mishandled bags?

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 both sound an alarm in the presence of smoke is ________.