Exam 5: Discrete Probability Distributions

In a binomial distribution,

TABLE 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 Table 5-1,the probability that both sound an alarm in the presence of smoke is ________.

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

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,at most three of the cars have non-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. -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 ________.

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 variance for the number of retransmissions 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 probability that she does not get audited is ________.

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 all of the new employees will be from University B?

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 expected value gain for the house in neighborhood A?

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 70% 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 5-7 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?

True or False: The variance of the sum of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.

A campus program evenly enrolls undergraduate and graduate students.If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building,what is the probability that all 4 students selected are undergraduate students?

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 70% of your money on the house in neighborhood A and the remaining on the house in neighborhood B,what is the portfolio expected return 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,what is your expected profit when Design B is chosen?

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 less than two and more than eight mishandled bags?

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 probability that she gets audited at least once is ________.

True or False: 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.

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 ________.

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 no more than four mishandled bags?