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# Probability

### Mean and Standard Deviation of Randon Variable

The random variable x with probability distribution given below X = 2 3 4 7 10 P(x) = 0.1 0.2 0.4 0.1 0.2 (a) Determine the expected value of x (b) Determine the standard deviation of x (c) Given a sample size of 65, with sample me

### Probability of Outcome

A fair die is rolled two times. Let A be the event that the outcome of the first roll is an odd number. Let B be the event that the outcome of second roll is at least 5. A) What is the probability that the outcome of the second roll is at least 5, given that the first roll is an odd number? B) Are A and B independent? Why o

### Probability of a Suspect

The police are looking for a man who wears size 12 shoes and drives a black car. They estimate that 1 in 10 men wears size 12 shoes, and that 1 in 8 men drives a black car. If one man is chosen at random, what is the probability that he matches the description.

### Probability Of Required University Score

A prestigious university requires a score of at least 750 on a graduate exam for admission to its MBA program. Suppose the graduate exam is normally distributed with a mean of 500 and a standard deviation of 200. If a test taker is randomly selected, what is the probability he or she scores 750 or better?

### Production under normally distributed process

A production process manufactures items with weights that are normally distributed with mean 16 pounds and standard deviation 0.15 pound. An item is considered to be defective if its weight is less than 15.8 pounds or greater than 16.2 pounds. Suppose that these items are currently produced in batches of 200 units. [Hint: F

### Developing Decision Trees and Payoffs

How to develop a decision tree and the payoffs using the information given The Problem: Joe Morgan, an investment strategist has learned of a couple alternatives that his company can invest in. His firm has chosen to invest in real estate. Occasionally the firm will invest in commercial real estate, but mostly in residenti

### Binomial and Poisson Probability Distributions

Suppose you, as the manager of Tennessee Grilled Pork. would like to ensure you have enough cleaning staff for your dining room and would like to analyze data for customers who enter the restaurant to place and order and either eat in the restaurant or take their order to- go. If the probability that a customer will stay in the

### Continuous random variable

probability density function - f(x) = { x^2/ 9 , 0<x<3 (x is greater than or EQUAL to 0 and less than or EQUAL to 3) { 0, otherwise Let Y= 9X/5 + 32. Find E(Y) and STD(Y).

### Probability: Random Sampling

Sample question: A study of the effect of college education on job satisfaction was conducted. A contingency table is presented below: Satisfied with job Not satisfied with job Total Attended College 325 190 515 Did not Attend 186 369 555 Total 511 559 1070

### Using Probability to Determine Likelihood

At a gathering consisting of ten men and twenty women, two door prizes are awarded. Find probability that both door prizes are won by men. The winning ticket is not replaced, is this event likely or unlikely to occur?

### Soft Drink Preferences of People in Different Age Groups

Can I have help solving this problem? The table below shows the soft drinks preferences of people in three age groups. cola Root beer Lemon-line Under 21 years of age 40 25 20 Between 21 and 40 35 20 30 Over 40 years of age 20 30 35 If one of the 255 subjects i

### The probability associated with clothing orders

1. Orders for clothing from a particular manufacturer for this year's Christmas shopping season must be placed in February. The cost per unit for a particular dress is \$20 while the anticipated selling price is \$50. Demand is projected to be 50, 60, or 70 units. There is a 40 percent chance that demand will be 50 units, a 50 per

### Probability Distributions For Continuous Variables

A large company is planning to launch a new product in the market. However, the company is not sure about the state of the economy and its impact on the return on the capital investment associated with this new product. A key analysis in this regard is the expected return and risk. Since the new product can come in three differe

### Statistical Analysis: Annual Return

1. Suppose the annual return on XYZ stock follows a normal distribution with mean 0.12 and standard deviation 0.30. a. What is the probability that XYZ's value will decrease during a year? b. What is the probability that the return on XYZ during a year will be at least 20%? c. What is the probability that the return on

### Calculating the Probability in Random Samples

#25. Companies often make flextime scheduling available to help recruit and keep women employees who have children. Other workers sometimes view these flextime schedules as unfair. An article in USA Today indicates that 25% of male employees state they have to pick u the slack for moms working flextime schedules. Suppose you s

### Using Probability in Court Trials

1. In 1972, Rodrigo Partida, a Mexican-American, was convicted of burglary with intent to commit rape. His conviction took place in Hidalgo County, which is in Texas on the border with Mexico. In Hidalgo County, 79.1% of the residents eligible for jury selection are Mexican-American. Partida's conviction was later overturned bec

### The probability of off-the-job accidents in a sample size of 50

The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost \$200 billion annually in lost productivity (National Safety Council, March 2006). Based on NSC estimates, companies with 50 employees are expected to average three employee off-the-job accidents per year. Answer the following quest

### Bayers Theorem

Choose any medical scientific study who applied a Bayer Theorem and write down the article information (title, author, location, and date) of the article, write a paragraph about the summary or overview of the article (You can copy from the article), and write your opinion about the article.

### Essentials of Statistics for Business and Economics: Probability

((Essentials of Statistics for Business and Economics 6th Editionin)) In Chapter 5 Problem 33 33. 12 of the top 20 finishers in the 2009 PGA Championship at Hazeltine National Golf Club in chcaska, Minnesota used a Titleist brand golf ball (GolfballTest website, November 12, 2009.) Suppose this results are representaive of t

### The failure of the Space Shuttle Challenger

The January 1986 mission of the Space Shuttle Challenger was the 25th such shuttle mission. It was unsuccessful due to an explosion caused by an O-ring seal failure. (a) According to NASA, the probability of such a failure in a single mission was 1/ 63,000. Using this value of p and assuming all missions are independent, cal

### Binomial random variable and binomial distribution

Suppose that x is a binomial random variable with n = 5, p = 0.2, and q = 0.8. (a) For each value of x, calculate p(x), and graph the binomial distribution. (Round final answers to 5 decimal places.) p(0) = , p(1) = , p(2) = , p (3) = , p(4) = , p(5) = (b) Find P(x = 3). (Round final answer to 5 decimal pla

### Exercises in Statistics: Finding Equilibrium Quantity and Equilibrium Price

1. The difference between two numbers is twelve. Three times the smaller number is four less than twice the larger number. Find the smaller number. 2. John has \$20,000 to invest. As his financial consultant, you recommend that he invest in Treasury Bills that yield 5%, Treasury bonds that yield 7%, and corporate bonds that yi

### Sample Space & Probability

The manager of a small business receives a shipment of five hard drives. Three hard drives are good and 2 are defective. If a computer repair shop purchases 3 of these stock of hard drives from the small business and the selection was made at random: 1. List the elements of the sample space S using the letters G and D for g

### Site Preference for Restaurants

Suppose you manage Tennessee Grilled Pork, a fast food restaurant specializing in pork sandwiches and pork chops on a stick. You have decided to build a new restaurant and have 2 possible site locations (Site 1 and Site 2). Three groups of people make independent recommendations on site preference: the local management team, the

### Probability Relationships

Suppose you, as manager of Tennessee Grilled Pork, will submit proposals for a small business loan and a city business grant to help fund the building of the new location you submitted to the management teams. The probability of acquiring the small business loan is .79 and the probability of obtaining the city business grant is

### Statistical Analysis: Probability

1. Find the percentage of the total area under the standard normal curve between the given z-scores. a) Z=.64 and z =2.11 b) Z= -1.63 and z = -1.08 c) Z= - 2.91 and z = -.51 2. Find a z -score satisfying each of the given conditions a) 1% of the total area is to the left Z b) 25% of the total area is to the rig

### Determining Employee Expenditure Using Probability

If you are asked to calculate the probability that a randomly selected employee's expenditure is exactly \$5, what will be your answer? Why? Will your answer be the same for any individual expenditure? Assume that population of all employee expenditures follow a normal distribution. Could you set up an equation to find the z

### Qualitative vs. Quantitative

See the attached file. 1. Describe the following variables as quantitative or qualitative, and describe the scales of measurement. A.)The distance a student commutes from home to the Berkeley campus. B.)The rating of a stock as "strong buy," "buy," "hold," or "sell." C.)The percentage of alcohol (in volume) i

### Beginner's statistics

1. For each of the experiments described, let x determine a random variable and use your knowledge of probability to prepare a probability distribution . Use a tree diagram. Two dice are rolled and the total number of points is recorded. 2. According to the Web site of Mars, the makers of M&M'S plain chocolate candies, 2

### Probability and standard deviation calculations

1. A fair die is rolled 2 times. Let A be the event that the outcome of the first roll is an even number. Let B be the event that the outcome of the second roll be less than 2. a. What is the probability that the outcome of the second roll is less than 2 given that the first roll is an even number? b. Are A and B independ