Exam 5: Some Important Discrete Probability Distributions

Suppose the probability of a power outage at a nuclear power plant on a single day is the same every day of the year.Also the probability of having a power outage on a single day does not increase or decrease the probability of a power outage on another day.Which of the following distributions would you use to determine the probability that a power outage will occur next Monday?

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 most 2 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 probability of no retransmissions is ________.

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 neither sound an alarm in the presence of smoke is ________.

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 exactly 1 prefers Brand C 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,if you can invest half of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

What type of probability distribution will most likely be used to analyse warranty repair needs on new cars in the following problem? The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days.Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05.The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold.

Suppose that past history shows that 6% of college students prefer Brand A cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Brand A cola?

The Department of Commerce in a particular 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.

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 less than 5.0 or more than 8.0 chip parts?

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 standard deviation of the number of times she will be audited is ________.

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

On the average,1.8 customers per minute arrive at any one of the checkout counters of a grocery store.What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?

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 two mishandled bags?

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,exactly 2 of the cars have non-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 probability of at least one retransmission 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,no more than half of the cars have non-defective radios?

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 probability of at least 1 accident is ________.

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 exactly 4 prefer Brand C 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 for the house in neighbourhood B?