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# Probability

### Calculating Expected Return

I am planning on building an airport. There are only two parcels, labeled A and B on which the airport could feasibly be built. A corp. knows that once a parcel is chosen the cost of land near the airport will go up so they are considering buying land for an airport hotel adjacent to one of both of these parcels now before a sit

### Statistics - Combinations

1. An investment counselor would like to meet with 12 of his clients on Monday, but he has time for only 8 appointments. How many different combinations of the clients could be considered for inclusion into his limited schedule for that day? 2. The U.S. Department of Labor has reported that 30% of the 2.1 million mathematical

### Probability ... Please see the attached file.

A survey of employees at a large company found that following relative frequencies for the one-way distances they had to travel to arrive at work... Please see the attached file.

### Probability: a. If a die is rolled one time, classical probability would indicate that the probability of "two" should be 1/6. If the die is rolled 60 times and comes up "two" only 9 times, does this suggest that the die is "loaded"? Why or why not? b. if has been reported that about 35% of U.S. Adults attended a sports event during the previous year. What are the odds tat a randomly selected U.S. adult attended a sports event during the year?

A. If a die is rolled one time, classical probability would indicate that the probability of "two" should be 1/6. If the die is rolled 60 times and comes up "two" only 9 times, does this suggest that the die is "loaded"? Why or why not? b. if has been reported that about 35% of U.S. Adults attended a sports event during the p

### Probability ... (Please see the attached document)

1). You are tossing a die that has probability of 1/6 of coming up 1 on each toss. Tosses are independent. We are interested in how long we must wait to get the first 1. (a). The probability of a 1 on the first toss is 1/6. What is the probability that the first toss is not a 1 and the second toss is a 1? (b). What is the pr

### Scenario Questions ... (Please see the attached file)

Pam Beesly, the CEO's Administrative Assistant, has worked for Mr. Rump for a little over one year. She was originally hired by the Chief Operations Officer, Mr. Halpert, as his personal secretary but when the opening for the new assistant to the CEO became available (his last one, Marla, had to leave suddenly due to personal p

### Scenario Questions on Production of DVDs

Chief of Bruin Consulting Engineering Division, Dr. Dil Bert, is in charge of and overseeing the production of the company's DVDs. The DVDs are used to record the company's PSAs and then distributed to the local public access channels. Unfortunately, the Engineering Division's quality control is not up to the standards that th

### Basic probability questions involving intersections of events and events that are either independent events or mutually exclusive events.

Mr. Arthur Van De Lay, not only the company's Chief Information Officer, but also the reigning mid-west "Rock, Paper, Scissors" champion, has bid on two eco-friendly projects. Project "A" is a recycling of metals contract with the town of Bellevue, NE, and project "B" is the toxic clean up contract for Omaha, NE, city parks aft

### Interpretations of probability

Please see the attached file. 1) The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A denote the event {a, b, c} and B denote the event {c, d, e}. Determine the following: a) P(A) b) P(B) c) P(A') d) P(A U B) e) P(A n B) 2) If the last digit

### Probability Questions: Affirmative Action Programs

A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as affirmative action) and medical students admitted through regular criteria. It was found that the graduation rate was 94% for medical students admitted through special programs (based

### Determining Whether a Jury Selection Process Is Biased

Determining Whether a Jury Selection Process Is Biased Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to Table 5-1 and find the indicated probability. a. Using the probability values in Table 5.1, find the probability value that should be used for determi

### Identity Probability Distributions

In this exercise, determine whether a probability distribution is given. In the case where a probability distribution is not described, identify the requirements that are not satisfied. In the case where a probability distribution is described, find its means and standard deviation. Mortality Study For a group of four men,

### Statistics - Poisson Distribution for Failure Rate

Given 5,000 light bulbs from an outside supplier. If past performance data indicates that these have been 3% defective, and a random sample of 40 parts are drawn from the shipment what is the probability that you will find more than 2 defective parts? Use the Poisson distribution to answer this question.

### Find binomial probabilities

Population of consumers where 30% of them favored a new product and 70% of them disliked it. If 20 persons are sampled, what are the probabilities of finding: Binomial: 8 or fewer consumers who favor the product. Precisely 10 consumers who favor the product. Fewer than 6 consumers who favor the product. More than 7 consumers who

### probability of a binomial distribution

It was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with 6 different professors. a) What is the probability that all 6 are extroverts? b) What is the probability that none of your professors are extroverts? c) What is the probability that at least 2 of your prof

### Determining Probability and Standard Deviation: Crime Example

Does crime Pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes , the criminals are never found and the case is never solved. Suppose that a neighborhood district in a large city has repeated property crimes, not always by the same criminals. The police are investigating six property crimes cas

### probability of Poisson distribution

Accidents at a chemical plant occur at a rate of 1.9 per month. Find: The expected number of accidents in a year? The probability of no accidents next month? The probability of fewer than three accidents next month?

### Determining Probability: Dating Questions

James Burke claims that about 70% of all single men would welcome a women taking the initiative in asking for a date. A random sample of 20 single men were asked if they would welcome a women taking the initiative in asking for a date. What is the probability that come a women taking the initiative in asking for a date. What is

### Binomial probabilities - Trevor is interested in purchasing the local hardware/sporting goods in the small town of Dove creek, Montana. After examing accounting records for the past several years, he found that ...

Trevor is interested in purchasing the local hardware/sporting goods in the small town of Dove creek, Montana. After examing accounting records for the past several years, he found that the store has been grossing over \$850 per day about 60% of the business days it is open. Estimate the probability that the store will gross over

### Random variables and probabilities distributions

Age range(yr)| 20-29 30-39 40-49 50-59 60-69 70-79 80+ Midpoint | 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of | 5.7 9.7 19.5 29.2 25.0 9.1 1.8 nurses a) Using the age midpoints x and the percentages of of nurses, do we have a valid probability distribution? Explain. b)

### Statistics - Probability Questions

1.Typographical and spelling errors can be either "nonword errors" or "word errors." A nonword error is not a real word, as when "the" is typed as "teh." A word error is a real word, but not the right word, as when "lose" is typed as "loose." When undergraduates are asked to write a 250 word essay (without spell checking), the

### Normal Distribution - Scores on an examination are assumes to be normally distributed with mean 78 and ... (Please see the attached document)

Please solve the following problem: Scores on an examination are assumes to be normally distributed with mean 78 and variance 36. a.What is the probability that a person taking the examination scores higher than 72? b.Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is th

### Determining the Value of P: Production Line Example

A production line manager, J, is trying to design a manufacturing line, using the machines that her company already has. Based on the historical records, each individual candidate machine will fail, during the production, with a probability of 1-p, and their failures are independent. Since the company plans to discard the machin

### Pedestrian Walk Buttons (Probability) - Pedestrian Walk Buttons New York City has 750 pedestrian walk buttons that work, and ...

Pedestrian Walk Buttons New York City has 750 pedestrian walk buttons that work, and another 2500 that do not work (based on data from "For Exercise in New York Futility, Push Button," by Michael Luo, New York Times). If a pedestrian walk button is randomly selected in New York City, what is the probability that it works? Is

### Probability(Combinations)

Question: An office furniture manufacturer makes filing cabinets. It offers customers 2 choices for the base and 4 choices for the top, and 5 different heights. A customer may choose any combination of the 5 different-sized modules so that the finished filing cabinet has a base, a top, and 1, 2, 3, 4, 5, or 6 storage module

### Probability - Genetics Cystic fibrosis is a recessive trait

Cystic fibrosis is a recessive trait in humans. a. If two people are heterozygous for cystic fibrosis and they have 3 kids, what is the probability that one of these will have cystic fibrosis? b. What is the probability that only the first child will have cystic fibrosis? c. What is the probability that they will hav

### Permutations: Different Ways the Winners Can Be Drawn

In the cash now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousands dollars, and the third prize is ten thousand dollars. Use the permutations rule to determine th

### Compound events: Dice example

You roll two fair dice, a green one and a red one. a) Are the outcomes on the dice independent? b) Find P(1 on green die and 2 on red die). c) Find P (2 on green die and 1 on the red die). d) Find P(1 on green die and 2 on red die) or (2 on green die and 1 on red die).

### Determining Probability of Random Variable: Example Problem

Find the probability that a standard normal random variable will assume a value between: a. z = 1.5 and z = .75 b. Greater than 1.25 c. Find a z such that 70% of the area is above that value.

### Elementary Probability Theory: Botanist Example Problems

Elementary Probability Theory: A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant.To estimate the probability that a new plant will germination, a random sample of 3000 seeds was planted