Exam 5: Some Important Discrete Probability Distributions

A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.025.To find the probability that exactly 20 of the computers will require repair on a given day,one will use what type of probability distribution?

Instruction 5.4 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently. -Referring to Instruction 5.4,which distribution would you use to determine the probability that all the smoke alarms will function properly in case of a fire?

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the covariance of the two houses?

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 at least 3 power outages in a year is ______.

Instruction 5.6 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 5.6,what is the probability that any particular biscuit being inspected has fewer than 5.0 chip parts?

If the covariance between two investments is zero,the variance of the sum of the two investments will be equal to the sum of the variances of the investments.

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,what is the standard deviation of the value gain for the house in neighbourhood B?

A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts.Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week.Interpret this value.

Instruction 5.3 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 0.25 -\ 22,500 \ 30,500 0.40 \ 10,000 \ 25,000 0.35 \ 40,500 \ 10,500 -Referring to Instruction 5.3,if you can invest 10% 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?

It was believed that the probability of a small business that declared bankruptcy per month was the same in any month.Also the number of small businesses that declared bankruptcy was the same every month.Which of the following distributions would you use to determine the probability that more than three bankruptcies will occur next month?

Instruction 5.7 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 5.7,what is the probability that in the next 1,000 customers,the airline will have no more than three mishandled bags?

If the outcomes of a random variable follow a Poisson distribution,then their

In a game called Taxation and Evasion,a player rolls a pair of dice.If on any turn the sum is 7,11 or 12,the player gets audited.Otherwise,she avoids taxes.Suppose a player takes five turns at rolling the dice.T -he probability that she does not get audited is ______.

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8.You have five such alarms in your home and they operate independently.Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?

Instruction 5.7 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 5.7,what is the probability that in the next 1,000 customers,the airline will have no mishandled bags?

Suppose that past history shows that 60% of university students prefer Brand C cola.A sample of five students is to be selected. -The probability that exactly one prefers Brand C is ______

Instruction 5.2 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth. X 0 1 2 3 4 5 0.1 0.2 0.4 0.1 0.0 0.0 P(X) 0 0 5 5 5 5 -Referring to Instruction 5.2,the variance of the number of accidents is ______

The online access computer service industry is growing at an extraordinary rate.Current estimates suggest that only 20% of the home-based computers have access to online 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 online services.

Thirty-six of the staff of 80 teachers at a local high school are certified in cardiopulmonary 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?

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 at least 1 power outage in a year is ______.