Exam 5: Discrete Probability Distributions

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.

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 total variance of the profit if you add more shifts to your production lines and choose to produce both designs?

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 variance of your profit when Design B is chosen?

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 70% of the production lines and Design B for the remaining production lines, what is the coefficient of variation of your investment?

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

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, if you can invest 30% 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?

SCENARIO 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 network. -Referring to Scenario 5-3, the probability of at least one retransmission is ________.

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 ________.

SCENARIO 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 mean number of bad bulbs per shift is 6.0. -Referring to Scenario 5-6, what is the probability that any shift being inspected has less than 5.0 or more than 8.0 bad bulbs.

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?

Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio- Pulmonary Resuscitation (CPR).In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

SCENARIO 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 Scenario 5-10, what is the probability that none of the new employees will be from University A?

SCENARIO 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest. -Referring to Scenario 5-4, the probability of 3 accidents is ________.

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Prices for 100 rats follow the following distribution: How much should the lab budget for next year's rat orders be, assuming this distribution does not change?

A probability distribution is an equation that

The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.The probability of seven or eight 911 calls in a day 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, the table above is called the ______________ for the two designs.