Exam 5: Some Important Discrete Probability Distributions

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

Instruction 5-5 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Instruction 5-5,if you can invest 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio expected return of your investment?

What type of probability distribution will most likely be used to analyse the number of chocolate chip parts per biscuit in the following problem? The quality control manager of Marilyn's Biscuits is inspecting a batch of chocolate chip biscuits.When the production process is in control,the average number of chocolate chip parts per biscuit is 6.0.The manager is interested in analysing the probability that any particular biscuit being inspected has fewer than 5.0 chip parts.

Instruction 5-7 The quality control manager of Marilyn's Biscuits is inspecting a batch of chocolate chip biscuits.When the production process is in control,the average number of chocolate chip parts per biscuit is 6.0. -Referring to Instruction 5-7,what is the probability that any particular biscuit being inspected has fewer than 5.0 chip parts?

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4.Find the probability that more than 3 bankruptcies occur next month.

Suppose that past history shows that 60% of university students prefer Brand C cola.A sample of 5 students is to be selected.The probability that exactly 3 prefer Brand C is ________.

A campus program evenly enrols 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?

Another name for the mean of a probability distribution is its expected value.

Suppose that a judge's decisions follow a binomial distribution and that his verdict is correct 90% of the time.In his next 10 decisions,the probability that he makes fewer than 2 incorrect verdicts is 0.736.

Instruction 5-5 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Instruction 5-5,if your investment preference is to maximise your expected return while exposing yourself to the minimal amount of risk,will you choose a portfolio that will consist of 10%,30%,50%,70%,or 90% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B?

Which of the following about the binomial distribution is NOT a true statement?

The on-line access computer service industry is growing at an extraordinary rate.Current estimates suggest that only 20% of the home-based computers have access to on-line services.This number is expected to grow quickly over the next 5 years.Suppose 25 people with home-based computers were randomly and independently sampled.Find the probability that more than 20 of those sampled currently do NOT have access to on-line services.

Instruction 5-8 A major airline keeps a record of the number of mishandled bags per 1,000 customers.In 2011,the airline had 4.06 mishandled bags per 1,000 customers.Assume that the number of mishandled bags has a Poisson distribution. -Referring to Instruction 5-8,what is the probability that in the next 1,000 customers,the airline will have no mishandled bags?

A national trend predicts that women will account for half of all business travellers in the next 3 years.To attract these women business travellers,hotels are providing more amenities that women particularly like.A recent survey of Australian hotels found that 70% offer hairdryers in the bathrooms.Consider a random and independent sample of 20 hotels.Find the probability that at least 9 of the hotels in the sample do NOT offer hairdryers in the bathrooms.

The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

The portfolio expected return of two investments

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 exactly 3 power outages in a year is ________.

Instruction 5-5 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Instruction 5-5,what is the covariance of the two houses?

A national trend predicts that women will account for half of all business travellers in the next 3 years.To attract these women business travellers,hotels are providing more amenities that women particularly like.A recent survey of Australian hotels found that 70% offer hairdryers in the bathrooms.Consider a random and independent sample of 20 hotels.Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

Instruction 5-5 There are two houses with almost identical characteristics available for investment in two different neighbourhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: Returns Probability Neighbourhood A Neighbourhood B .25 -\ 22,500 \ 30,500 .40 \ 10,000 \ 25,000 .35 \ 40,500 \ 10,500 -Referring to Instruction 5-5,what is the variance of the gain in value for the house in neighbourhood A?