Exam 5: Discrete Probability Distributions

TABLE 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Table 5-8,if you decide to choose Design A for 10% of the production lines and Design B for the remaining production lines,what is the coefficient of variation of your investment?

TABLE 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 Table 5-7,if you can invest 90% 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?

TABLE 5-8 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants.Your profit (in thousands of dollars)will depend on the taste of the consumers when winter arrives.The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. -Referring to Table 5-8,if you decide to choose Design A for 70% of the production lines and Design B for the remaining production lines,what is the coefficient of variation of your investment?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The variance of the number of power outages is ________.

If π remains constant in a binomial distribution,an increase in n will not change the mean.

From an inventory of 48 new cars being shipped to local dealerships,corporate reports indicate that 12 have defective radios installed.Which of the following distributions would you use to determine the probability that out of the 8 new cars it just received that,when each is tested,no more than 2 of the cars have defective radios?

TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis,Oregon. -Referring to Table 5-4,the probability of at least 1 accident is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that fewer than 2 prefer Brand C is ________.

A probability distribution is an equation that

The number of 911 calls in Butte,Montana,has a Poisson distribution with a mean of 10 calls a day.The probability of seven 911 calls in a day is ________.

TABLE 5-6 The quality control manager of Green Bulbs Inc.is inspecting a batch of energy saving compact fluorescent light bulbs.When the production process is in control,the average number of bad bulbs per shift is 6.0. -Referring to Table 5-6,what is the probability that any particular shift being inspected has less than 5.0 or more than 8.0 bad bulbs.

TABLE 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers.In a recent year,the hotel chain had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Table 5-9,what is the probability that in the next 1,000 customers,the hotel chain will have between two and four inclusive mishandled bags?

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 hypergeometric distribution.

Suppose that past history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 4 prefer Brand C is ________.

TABLE 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 Table 5-7,what is the variance of the gain in value for the house in neighborhood B?

TABLE 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 Table 5-10,what is the probability that two of the new employees will be from University A?

TABLE 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 Table 5-5,what is the probability out of the 8 new cars it just received that,when each is tested,exactly half of the cars have defective radios?

TABLE 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. -Referring to Table 5-3,the probability of at least one retransmission is ________.

TABLE 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. -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 expected number of times she will be audited is ________.

If π remains constant in a binomial distribution,an increase in n will increase the variance.