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Probability

Probability in the resolution of marketing problems

Name a workplace example that show how data collection and representation facilitate probability in the resolution of marketing-related or business problems? Outside of gambling, what wide-spread activities are governed by the binomial probability distribution? Are the results of these activities gathered and analyzed or are

To determine probability using probability tree

The Senate consists off 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability t

Probability of smokers: hospital case

A large research hospital has accumulated statistical data on its patients for an extended period of time. Researchers have determined that patients who are smokers have an 18% chance of contracting a serious illness such as heart disease, cancer, or emphysema, whereas there is only a .06 probability that a non smoker will cont

Shopping Probability Problem

Each Saturday a shopper visits one of three possible stores. She goes to Store A with probability ½, to Store B with probability ¼, and to Store C with probability ¼. If she goes to Store A there is a 60% chance that she will make a purchase. The corresponding figures for Stores B and C are 20% and 40% respectively. (i) What

Probability Problems: Normal distribution, Binomial distribution.

A)The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. a) what is the area between 415 pounds and the mean of 400 pounds? b) what is the area between the mean and 395 pounds? c) what is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?

Distribution for Sales Product

Please explain the steps in details so I can understand how the answers are derived: A retail store experiences the following probability distribution for sales of a product. Sales (units) 0 1 2 3 4 5 6 Probability 0.08 0.12 0.28 0.24 0.14 0.10 0.04 a .Set up intervals of random numbers that can be used

What is the probability?

A) The Ludlow Wildcats baseball team, a minor league team in the Cleveland Indians orgainzation, plays 70 precent of their games at night and 30 percent during the day. The team wins 50 percent of their night games and 90 percent of their day games. According to today's newspaper, they won yesterday. What is the probability

Statistical Probability Calculations

Please contribute your analysis and comment. Credit card companies have aggressively solicited new accounts from students who are new homeowners. Suppose that a sample of 150 new homeowners indicated the following information as to whether they possessed a Visa Card or an American Express Card.

Basic Statistical Probability

1. The personnel department at Hayes Air West is interested in studying the monthly applicant flow for our entry level service jobs. Find the mean and st. deviation for the following frequency distribution: Job applicants/month f 78-85 45 86-93 78 94-101 115 102-109 40 110-117 15 118-125 4 Mean: St. Dev.: 2. Given

Life Insurance Policy Payout Probability

The probability that Traci Muldone will die during the 10-year term of a life insurance policy is assessed by the insurance company at 1/5. Arthur Average's probability of living to the end of the 10-year period is reckoned at 95% What is the probability that at the end of the 10 years (a) both (b) one or the other, but not bo

Computing sample standard deviations

1. Compute the sample standard deviation of the data set 6,4,2,1,4,1 2. A test has 6 multiple choice questions, each with 4 alternatives. What is the probability of guessing 5 or more questions correctly?

Some t/f probability i.r.v questions

Some straightforward questions relating to i.r.v's and their expectation/variance/conditional densities. See attached file for full problem description.

Probability: Gaussian Random Variables

1.If X is a Gaussian random variable with zero mean and variance equal to 1, then the density function of Z = is equal to 2fx(z), z ≥ 0. 2. The sum of a random number of independent Gaussian random variables with zero mean and unit variance results in a Gaussian random variable regardless of the distribution of N (the nu

10 Probability Problems

(See attached file for full problem description) --- 1. Given the probability function P(x)=(2x-1)/16, for x=1,2,3,4. a. Write the probability distribution: b. Find the U (pop. mean) c. Find the O (pop. SD) 2. The number of cars to be worked on by a mechanic at ABC garage is a random represented x. The probability dist

Normal Distributions and Sample Means

The fill amount of bottles of soft drinks has been found to be normally distributed with a mean of 2.0 liters and a standard deviation of 0.05 liter. If a random sample of bottles is selected, what is the probability that the sample mean will be between 1.99 and 2.0 liters? A. 0.4772 B. 0.5228 C. 0.9544 D. Cannot be deter

T3-22

An on the job injury occurs once every 10 days on average, at an auto plant. WHat is the probability that the next on the job injury will occur within 10 days? A. .9513 B. .8647 C. .6500 D. .6321

T3-20

The probability that a standard normal random variable, Z, is between 1.00 and 3.00 is: A. 0.1574 B. 0.3158 C. 0.5456 D. 0.9544

Probability of Community and Diabetes

3. If the probability of a skin diver in a certain community having untreated diabetes is 0.15, what is the probability that two totally unrelated skin divers from the community do not have untreated diabetes? (Assume independence) 4. A shipment of 100 tires from the Apex Tire Corporation is known to contain 20 defective tire

Binomial Probability

Suposse I have a die with just 3 faces: Face A, Face B and Face C. I will throw it 50 times. I want to know how to calculate, what the odds are of getting 30 Face A (after the 50 attempts).

Probability of Hamburger or Chicken Preference

A survey is taken among customers of a fast food resturant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger. What is the probability that a randomly selected individual

Probability that a Surveyed Employee Picked has a Spouse & Degree

The employees of a company were surveyed on questions regarding their education background and martial status. Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is: A. 40/600 B. 340/600

Limit Moment-Generating Functions

Let S^2 be the sample variance of a random sample of size n from N (mean, standard deviation). Show that the limit, as n -> infinity , of the moment -generating function of e^sigma2t. Thus, in the limit, the distribution of S^2 is degenerate with probability 1 at sigma^2 . (See attached file for full problem description

Statistics Matlab Project : Simulate the Number Pi

5. 'Simulate the number pi'. Simulate n uniformly distributed random points in the square K={?1<x<1. ?1<y<1} Determine the number of points, m, that fall into the unit disk x2+y2 < 1. Note that the probability for a random point to be in the unit disk is pi/4. By the law of large numbers we expect m/n converges to pi/4 as n-->

Statistics

4. An article in Annals of Mathematical Statistics reports the following data on the number of borers in each of 120 groups of borers. Does the Poisson pmf provide a plausible model for the distribution of the number of borers in a group? (Hint: Add the frequencies for 7,8,..., 12 to establish a single category "> 7"). No.

Binomial Option Pricing, Black Scholes Option Pricing

5) Binomial Option Pricing: Suppose we live in a 3 period Black-Scholes world, t=0,1,2 whichidentify as follows. There is a stock with price S(0)= 1 in period 0.In each period , t=1,2, the price can either go up to u. S or down to d.S. Suppose u=1.2 and d=0.9. Suppose that the interest rate is constant at 4%. A) What i

7 Basic Probability Problems

1. A certain coin has the same probability of landing heads as it does landing tails - but this coin is special, because it also has a 30% chance of landing on its side. a. What is the probability of this coin landing heads? b. What are the odds against this coin landing on its side? c. If this coin is tossed twice, what is t

Analyzing Poisson Distribution

I would be grateful for an explanation to the following problem. Given that X possesses a Poisson distribution with mean u, show that the moment generating function of X is given by M(z)=exp(ue^z - u).

Calculating probabilities

For people with a certain disease, the length of time Y spent in remission is described by the following pdf f(y) = (1/9)y^2, 0<=y<=3 where Y is measured in years. What is the probability that a patient's remission lasts longer than 1 year?

Statistics question: Probability problems

1. An investor owns three common stocks. Each stock, independent of the other, has equally likely chances of: (1) increasing in value, (2) decreasing in value, (3) remaining the same value List the possible outcomes of this experiment. Estimate the probability at least two of the stocks increase in value.