Exam 5: Discrete Probability Distributions

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

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 customer,the hotel chain will have no more than three mishandled bags?

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 covariance of the two houses?

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 all of the hotels in the sample offered hairdryers in the bathrooms.

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The average number of airplanes arriving per minute is 3.The probability that exactly 6 planes arrive in the next minute is 0.05041.

In a Poisson distribution,the mean and variance are equal.

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 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 average number that you would expect to prefer 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 90% of the production lines and Design B for the remaining production lines,what is the coefficient of variation of your investment?

A stock analyst was provided with a list of 25 stocks.He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days.In reality,the prices of only 5 stocks would rise by more than 20% after 30 days.If he randomly selected 3 stocks from the list,he would use what type of probability distribution to compute the probability that all of the chosen stocks would appreciate more than 20% after 30 days?

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 at least two mishandled bags?

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 more than eight mishandled bags?

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?

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.

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 5-6 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.

If n = 10 and π = 0.70,then the mean of the binomial distribution is

Whenever π = 0.5,the binomial distribution will

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 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent). -Referring to Table 5-2,the probability that all 3 businesses fail is ________.