Exam 5: Some Important Discrete Probability Distributions

Suppose that past history shows that 60% of university students prefer Brand C cola.A sample of five students is to be selected. -The probability that exactly four prefer Brand C is ______

A certain type of new business succeeds 60% of the time.Suppose that three such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).Which of the following distributions would you use to determine the probability that all of them will fail?

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,if your investment preference is to maximise your expected return while exposing yourself to the minimal amount of risk,will you choose a portfolio that will consist of 10%,30%,50%,70% or 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B?

Instruction 5.4 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 two such alarms in your home and they operate independently. -Referring to Instruction 5.4,the probability that both sound an alarm in the presence of smoke is ______

Instruction 5.7 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 5.7,what is the probability that in the next 1,000 customers,the airline will have at least two mishandled bags?

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?

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 five turns at rolling the dice. -The probability that she gets audited at least once is ______.

Instruction 5.7 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 5.7,what is the probability that in the next 1,000 customers,the airline will have less than two and more than eight mishandled bags?

What type of probability distribution will most likely be used to analyse the number of chocolate chip parts per biscuit in the following problem? 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.The manager is interested in analysing the probability that any particular biscuit being inspected has fewer than 5.0 chip parts.

Instruction 5.8 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Instruction 5.8,what is the probability out of the eight new cars it just received that,when each is tested,exactly two of the cars have non-defective radios?

Instruction 5.5 A certain type of new business succeeds 60% of the time. Suppose that three 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 5.5,the probability that at least one business succeeds 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 five turns at rolling the dice. -The variance of the number of times she will be audited is ______.

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the expected value gain for the house in neighbourhood B?

Instruction 5.1 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 5.1,the standard deviation of the number of retransmissions is ______.

The covariance between two investments is equal to the sum of the variances of the investments.

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the expected value gain if you invest in both houses?

Instruction 5.8 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Instruction 5.8,what is the probability out of the eight new cars it just received that,when each is tested,no more than half of the cars have defective radios?

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the standard deviation of the value gain for the house in neighbourhood A?

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.

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