Exam 5: Discrete Probability Distributions

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 variance of the number of accidents is _____.

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 911 calls in a day is _____.

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 the hotels in the sample offered hairdryers in the bathrooms.

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?

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 5-9 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 at least two mishandled bags?

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 more than eight mishandled bags?

The portfolio expected return of two investments

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 produced between 5.0 and 8.0 inclusive bad bulbs.

SCENARIO 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 Scenario 5-5,what is the probability out of the 8 new cars it just received that,when each is tested,at most three of the cars have non-defective radios?

SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month.Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month. -Referring to Scenario 5-11,what is probability that at least five security transactions will be conducted in one month?

SCENARIO 5-1 The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have 2 such alarms in your home and they operate independently. -Referring to Scenario 5-1,the probability that at least one sounds an alarm in the presence of smoke 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 risk of your investment?

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 5-4 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 standard deviation of the number of accidents is _____.

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 at least 1 of the members chosen for the team have some prior competition experience?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The probability that there will be no more than 1 power outage in a year is _____.

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 more than four mishandled bags?

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 all 3 businesses fail 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 70% of the production lines and Design B for the remaining production lines,what is the risk of your investment?