Exam 5: Discrete Probability Distributions

Which Excel function can be used to calculate the expected value for a discrete random variable?

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?

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 mean or expected value of the number of accidents is ________.

SCENARIO 5-10 An accounting firm in a college town usually recruits employees from two of the universities in town.This year, there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Scenario 5-10, what is the probability that at least two of the new employees will be from University B?

The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year.The variance of the number of power outages is ____________.

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7, what is the variance of the gain in value for the house in neighborhood B?

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 do not have access to on-line services.

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 ________.

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7, if your investment preference is to maximize 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 neighborhood A and the remaining on the house in neighborhood B?

A professor receives, on average, 24.7 e-mails from students the day before the midterm 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 n = 10 and then the standard deviation of the binomial distribution is

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.

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7, if your investment preference is to minimize the amount of risk that you must take and do not care at all about the expected return, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

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

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 5 turns at rolling the dice.The variance of the number of times she will be audited 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 that at least 9 of the hotels in the sample do not offer 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 30% of the production lines and Design B for the remaining production lines, what is the coefficient of variation of your investment?

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.

A stock analyst was provided with a list of 25 stocks.He was expected to pick 3 stocks from the list whose prices are expected to rise by more than 20% after 30 days.The prices of only 5 stocks would rise by more than 20% after 30 days.If he randomly selected 3 stocks from the list, he would use what type of probability distribution to compute the probability that all the chosen stocks would appreciate more than 20% after 30 days?

SCENARIO 5-7 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition.The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-7, if you can invest 10% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio expected return of your investment?