Exam 5: Discrete Probability Distributions

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.If the committee members are chosen randomly,what is the probability that precisely half of the members will be women?

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 variance of the number of times she will be 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 at least two of the new employees will be from University B?

True or False: If remains constant in a binomial distribution,an increase in n will increase the variance.

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 ________.

If the outcomes of a variable follow a Poisson distribution,then their

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 standard deviation of the number of accidents is ________.

What type of probability distribution will most likely be used to analyze the number of blue chocolate chips per bag in the following problem? The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.When the production process is in control,the average number of blue chocolate chips per bag is 6.0.The manager is interested in analyzing the probability that any particular bag being inspected has fewer than 5.0 blue chocolate chips.

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?

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 risk of your investment?

The covariance

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 the total standard deviation of the profit if you increase the shift of your production lines and choose to produce both designs?

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 your investment preference is to maximize your expected profit while exposing yourself to the minimal amount of risk,will you choose a production mix that will consist of 10%,30%,50%,70%,or 90% of your production lines for Design A and the remaining for Design B?

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 none of the members chosen for the team have any competition experience?

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 half 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 5-4 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 mean or expected value of the number of accidents 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,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?

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 2 or fewer prefer brand C is ________.