Exam 5: Discrete Probability Distributions

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

If X has a binomial distribution with n = 5 and p = 0.1,then P(X = 2)= _____.

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 fewer than 10 of those sampled currently do not have access to on-line services.

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 probability of 3 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 more than four of the new employees will be from University A?

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?

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_____.

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 total standard deviation of value gain if you invest in both houses?

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 probability of at least 1 accident 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 2 or fewer prefer brand C is_____ .

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.

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 less than 5.0 or more than 8.0 bad bulbs.

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 fewer than four and more than eight employees are from the Utah plant?

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 half 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?

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

If $\pi$ remains constant in a binomial distribution,an increase in n will increase the variance.

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 fewer than six mishandled bags?

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?

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?

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 10% of the production lines and Design B for the remaining production lines,what is the risk of your investment?