Exam 5: Discrete Probability Distributions

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 exactly 1 business succeeds is _____.

Current estimates suggest that 75% of the home-based computers in a foreign country have access to on-line services.Suppose 20 people with home-based computers were randomly and independently sampled.Find the probability that more than 9 of those sampled currently have access to on-line services.

If n = 10 and $\pi$ = 0.70,then the standard deviation of the binomial distribution is

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 both sound an alarm in the presence of smoke is_____.

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 exactly ten security transactions will be conducted in one month?

SCENARIO 5-13 Bell Computers manufactures personal computers at two plants,one in Arkansas and one in Utah.The Arkansas plant has 50 employees;the Utah one has 40 employees.A random sample of 12 employees was selected to complete a job satisfaction questionnaire -Using scenario 5-13,what is the probability that fewer than four or more than eight employees completing the questionnaire are from the Utah plant?

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 probability of receiving exactly three calls in a 6-minute period?

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 standard deviation of your profit when Design A 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,the table above is called the for the two designs.

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.

A probability distribution is an equation that

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 probability of receiving exactly 10 calls in a 12-minute period?

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 at least 6.0 bad bulbs.

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 fewer than two security transactions will be conducted in one month?

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 standard deviation 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 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?

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?

SCENARIO 5-13 Bell Computers manufactures personal computers at two plants,one in Arkansas and one in Utah.The Arkansas plant has 50 employees;the Utah one has 40 employees.A random sample of 12 employees was selected to complete a job satisfaction questionnaire -Using Scenario 5-13,what is the probability that exactly five of the employees completing the questionnaire were from the Arkansas plant?

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 exactly 3 prefer brand C is_____ .

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 exactly 1 prefers brand C is_____ .