Exam 5: Discrete Probability Distributions

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 two and at least eight mishandled bags?

The local police department must write,on average,5 tickets a day to keep department revenues at budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day.Find the probability that less than 6 tickets are written on a randomly selected day from this population.

The local police department must write,on average,5 tickets a day to keep department revenues at budgeted levels.Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day.Find the probability that exactly 6 tickets are written on a randomly selected day from this population.

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?

If X has a binomial distribution with n = 5 and p = 0.1,then P(X = 2)= ________.

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,the table above is called the ________ for the two 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 you decide to choose Design A for 90% 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 two of the new employees will be from University A?

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 90% of the production lines and Design B for the remaining production lines,what is the coefficient of variation 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 two of the new employees will be from University B?

True or False: The largest value that a Poisson random variable X can have is n.

A national trend predicts that women will account for half of all business travelers in the next 3 years.To attract these women business travelers,hotels are providing more amenities that women particularly like.A recent survey of American hotels found that 70% offer hairdryers in the bathrooms.Consider a random and independent sample of 20 hotels.Find the probability that all of the hotels in the sample offered hairdryers in the bathrooms.

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 ________.

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 produced 4.0 bad bulbs?

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 your investment preference is to maximize your expected profit and not worry at all about the risk that you have to take,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?

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 10% 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 5-5 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 2 of the cars have defective radios?

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 none of the new employees will be from University B?

The number of 911 calls in Butte,Montana,has a Poisson distribution with a mean of 10.0 calls a day.The standard deviation of the number of 911 calls in a day is ________.