Exam 5: Discrete Probability Distributions

SCENARIO 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 Scenario 5-8,if you decide to choose Design A for half of the production lines and Design B for the other half,what is your expected profit?

SCENARIO 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 Scenario 5-9,what is the probability that in the next 1,000 customers,the hotel chain will have less than two and more than eight mishandled bags?

SCENARIO 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 Scenario 5-7,what is the expected value gain if you invest in both houses?

SCENARIO 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 Scenario 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?

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 exactly half of the members chosen for the team have some prior competition experience?

SCENARIO 5-2 A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete,so it is reasonable to believe that their relative successes would be independent). -Referring to Scenario 5-2,the probability that at least 1 business succeeds is_____ .

The variance of the sum of two investments will be equal to the sum of the variances of the two investments plus twice the covariance between the investments.

SCENARIO 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 Scenario 5-8,what is the covariance of the profits from the two different designs?

Suppose that history shows that 60% of college students prefer Brand C cola.A sample of 5 students is to be selected.The probability that fewer than 2 prefer brand C is _____.

SCENARIO 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 Scenario 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 coefficient of variation of your investment?

SCENARIO 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 Scenario 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 expected profit?

SCENARIO 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 Scenario 5-7,what is the standard deviation of the value gain for the house in neighborhood A?

SCENARIO 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 Scenario 5-9,what is the probability that in the next 1,000 customers,the hotel chain will have no mishandled bags?

SCENARIO 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 Scenario 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?

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

The largest value that a Poisson random variable X can have is n.

If X has a binomial distribution with n = 4 and p = 0.3,then P(X > 1)= _____.

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 mean number of blue chocolate chips per bag is 6.0.The manager is interested in analyzing the probability that any bag being inspected has fewer than 5.0 blue chocolate chips.

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 6.5 tickets per day.Interpret the value of the mean.

SCENARIO 5-12 Phone calls arrive at the rate of 50 per hour at the reservation desk for Queen City Airways.The desk manager has asked you for an analysis of the call rates and probabilities to better understand the operation and determine if more call desk workers are needed. -Using Scenario 5-12,What is the expected number of calls when calculating the probability of receiving nine calls in a 12-minute period?