Exam 5: Discrete Probability Distributions

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 5 such alarms in your home and they operate independently.Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?

A financial analyst is presented with information on the past records of 60 start-up companies and told that in fact only 3 of them have managed to become highly successful.He selected 3 companies from this group as the candidates for success.To analyze his ability to spot the companies that will eventually become highly successful,he will use what type of probability distribution?

Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

In a Poisson distribution,the mean and standard deviation are equal.

The Poisson distribution can be used to model a continuous random variable.

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?

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.

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?

Suppose the probability of a power outage at a nuclear power plant on a single day is the same every day of the year.Also the probability of having a power outage on a single day does not increase or decrease the probability of a power outage on another day.Which of the following distributions would you use to determine the probability that a power outage will occur next Monday?

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 fewer than six mishandled bags?

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 3 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 fewer than eight mishandled bags?

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 at least 1 prefers Brand C is ________.

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 half of the production lines and Design B for the other half,what is the coefficient of variation 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 the covariance of the profits from the two different 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,what is the variance of your profit when Design A is chosen?

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 ________.

It was believed that the probability of a small business that declared bankruptcy per month was the same in any month.Also the number of small businesses that declared bankruptcy was the same every month.Which of the following distributions would you use to determine the probability that more than 3 bankruptcies will occur next month?

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 5-10 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 six of the new employees will be from University A?