Exam 5: Some Important Discrete Probability Distributions

What type of probability distribution will the consulting firm most likely employ to analyse the insurance claims in the following problem? An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims.It is known that the industry proportion for false claims is 3%.The consulting firm has decided to randomly and independently sample 100 of the company's insurance claims.They believe the number of these 100 that are false will yield the information the company desires.

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

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 two or at least eight mishandled bags?

A university lecturer receives,on average,24.7 e-mails from students the day before the final exam.To compute the probability of receiving at least 10 e-mails on such a day,he will use what type of probability distribution?

If X has a binomial distribution with n = 4 and p = 0.3,then P(X = 1.= ______

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

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: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year's rat orders be,assuming this distribution does not change?

Suppose that the number of airplanes arriving at an airport per minute is a Poisson process.The average number of airplanes arriving per minute is three.The probability that exactly six planes arrive in the next minute is 0.0504.

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 more than three prefer Brand C is______.

For a probability distribution for a discrete random variable,the sum of the probabilities must equal 1.

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 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?

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 70% of your money on the house in neighbourhood A and the remaining on the house in neighbourhood B,what is the portfolio risk of your investment?

Instruction 5.8 From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. -Referring to Instruction 5.8,what is the probability out of the eight new cars it just received that,when each is tested,at most two of the cars have defective radios?

If n = 10 and p = 0.70,then the mean of the binomial distribution is

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

Instruction 5.1 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media. X 0 1 2 3 p(X) 0.35 0.35 0.25 0.05 -Referring to Instruction 5.1,the variance for the number of retransmissions is ______.

Instruction 5.1 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a double satellite media. X 0 1 2 3 p(X) 0.35 0.35 0.25 0.05 -Referring to Instruction 5.1,the probability of no retransmissions is ______.

On the average,1.8 customers per minute arrive at any one of the checkout counters of a grocery store.What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter?

Suppose that past history shows that 60% of university students prefer Brand C cola.A sample of five students is to be selected. -The average number that you would expect to prefer Brand C is ______

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 exactly five bankruptcies occur next month.