Exam 5: Discrete Probability Distributions

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students.Ten of the 15 students have no prior competition experience while the others have some degree of experience.What is the probability that at least 1 of the members chosen for the team have some prior competition experience?

An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women.Which of the following distributions would you use to determine the probability that half of the members will be women?

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

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 at least two 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,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 expected return 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 your investment preference is to maximize your expected return and not worry at all about the risk that you have to take,will you choose a portfolio that will consist of 10%,30%,50%,70%,or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

The number of 911 calls in Butte,Montana,has a Poisson distribution with a mean of 10 calls a day.The probability of 2 or more 911 calls in a day is ________.

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 at least one sounds an alarm in the presence of smoke is ________.

The online access computer service industry is growing at an extraordinary rate.Current estimates suggest that 75% of the home-based computers have access to online services.Suppose 20 people with home-based computers were randomly and independently sampled.Find the probability that fewer than 10 of those sampled currently have access to online services.

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.

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 5-7 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 standard deviation of the value gain for the house in neighborhood B?

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 expected profit?

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 mean or expected value for the number of retransmissions 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 more than 3 prefer Brand C 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 5-8 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 30% of the production lines and Design B for the remaining production lines,what is the 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 10% of the production lines and Design B for the remaining production lines,what is the risk of your investment?

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 no more than four of the new employees will be from University 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 your investment preference is to maximize 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 neighborhood A and the remaining on the house in neighborhood B?