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# Probability

### Probability - Department Stores (J C Penney, Macy's, and Sears)

A mall has three department stores, JC Penney, Macy's, and Sears. A survey of 2,118 people exiting the mall found that 433 made a purchase at JC Penney, 412 made a purchase at Macy's, 638 made a purchase at Sears, 109 made a purchase at JC Penney and Macy's, 167 made a purchase at JC Penney and Sears, 213 of them made a purchase

### The solution gives detailed steps on counting the ways for 2 specific questions using the combination techniques. All formula and calculations are shown and explained.

Suppose that there are a total of 19 students in an elementary school class. The teacher assigns each of the students a report on a mainland country in either North America or South America (not including the United States) and each student is assigned a different country. The North American countries that the teacher has to pic

### Explaining Basic Logic of Probability Theory

If i take a selective quantitative data for an example like it takes me 15 minutes to get to work everyday for 10 days how can/would i describe it. What is my ability to explain the basic logic of probability theory & my ability to identify the meaning of independent and dependent events

### Histograms, probability and random number range

I am working on a crew/asset planning problem that requires a discrete process generation table. The input data is shown in the histogram, and the required table format is shown. Please solve to fill the table data. Preferred format is Excel.

### Calculating the Probability for a Normal Random Variable

The ages of 50 women are approximately normally distributed with a mean of 48 years and a standard deviation of 5 years. One women is randomly selected from the group, and her age is observed. Find the probability that her age will fall between 56 and 59 years. Find the probability that her age will exceed 41 years.

### Finding Probabilities Under Normal Distribution

Suppose x is a normally distributed random variable with y=13 and o=2. Find the following probabilities: 1. P (x is greater than or equal to 13.5) 2. P (13.44 is less or equal to x and 18.18 is greater than or equal to x).

### Averages and Probability

The Wizard Tax Service is analyzing its operations during the month prior to the April 15 tax filing date. There is currently only one tax preparer at Wizard. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with and average time between arrivals of 12 minutes. When the tax

### Using Binomial Probability Distribution

1 Pan Thai Restaurant offers 5% discount if the customer pays in cash instead of paying by a credit card. Past evidence indicates that 30% of all customers pay in cash. During a day period 120 customers buy gasoline at this station. (a) What is the probability that at least 50 customers pay in cash? (b) What is the

### Applying the Probability Model

Please see attached files and use it to apply the questions if needed: 1) The definition of a probability model. Illustrate the two parts of the definition with an example selected from the worksheet. 2) Define the notion of independent events in a probability model. Using as your model the 36 element set of outcome

### Probability: High Risk Apartments

In a local town, there are three separate apartment blocks, A, B and C. Block A contains 10 apartments, of which two contain "High Risk" inhabitants. Block B contains eight apartments, with three occupied by "High Risk" inhabitants, and Block C contains 12 apartments, with four "High Risk" apartments. Assume that an apartment

### Probability Distribution: Learning Surveys

Learning is a lifetime activity. For some, it means learning from everyday experiences; for others, it means taking classes in a more traditional atmosphere. The percentage of people participating in organized learning situations during 2002 for each age group is reported here by NIACE. Age group:.........17-19...... 20-24.

### Markov Chain and Steady State Probabilities

1. A production process contains a machine that deteriorates rapidly in both quantity and output under heavy usage, so it is inspected at the end of each day. Immediately after inspection the condition of the machine is noted and classified into one of four possible states: State 0: good as new 1: Operable - minimum deteri

### Probability and Descriptive Statistics

Questions should be solved on excel file using excel functions. 1) Probabilities. A fair coin was tossed 3 times. Calculate the probabilities of the following 6 events. 1. Three heads were observed 2. Two heads were observes 3. One head were observed 4. At least two heads were observed 5. No more than two tails were o

### Statistics and Probability Distribution

Please show all of the steps and processes you used to solve each of the problems 1. Would you suspect that the IDEA surveys sent to South students each term could be biased in the responses received? Why or why not? 2.Using the data set below, please calculate the: 12 16 12 10 20 10 10 - Mean = - Median =

### Poisson Distribution: Birth-Death Process

The McDougal Sandwich Shop has two windows available for serving customers, who arrive at a Poisson rate of 40/hr. Service time is exponentially distributed with a mean of 2 min. Only one window is open as long as there are three or less customers in the shop. An identical server opens a second window when there are four or more

### Algebraic Worksheet

Please see attachment 1. The triangles are similar. Find the value of a. (See attached for diagram) A. 12 B. 6 C. 16 D. 10 2. In a survey, 480 people, or 75%, said they attended a movie at least once a month. How many people were surveyed? A. 360 people B. 555 people C. 405 people D. 640 people 3. Find P(

### Bayes Theorem - Decision Analysis - Type I & Type II Errors

See the attached file. Need step-by-step instructions on how to solve the following example problems: Decision Analysis The quality control manager in a chip manufacturing plant has to select one of two available quality control methods. The estimated error rates for the methods are presented below: (see attachment)

### Moment generating function and poisson distribution

** Please see the attached file for the complete solution ** Shirley runs a real estate company. She counts the total number of flats that she sells everyday. Let X_t be the total number of flats she sells on day t (t=1,2,...,7), and let X be the total number of flats she sells for the week. Suppose X_t are independent and iden

### Probability - Conditional Distribution, Law of total variance

A pollster wishes to obtain information on intended voting behavior in a two party system and samples a fixed number (n) of voters. Let X_1 ..., X_n denote the sequence of independent Bernoulli random variables representing voting intention, where E(X_l) = p, i = 1, ..., n (a) Suppose the number of voters n is fixed, compute

### Probability and Statistical Methods

1. A manufacturing intraocular lens is in a process of verifying a polishing machine. The polisher will be accepted only if the percentage of polished lenses containing surface defects does not exceed 1.5%.They took a sample of 300 lenses and found 5 lenses that had surface defect. Formulate a test appropriate for verification o

### Tree Diagram and Dice Tossing

Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Discuss the purpose of using such a visual in working out probability.

### Payoff Table and Optimal Strategy in decision making.

The president of a large oil company must decide how to invest the company's \$10 million of excess profit. He could invest the entire sum in solar energy research, or he could use the money to research better ways of processing coal so that it will burn more cleanly. His only other option is to put half of this R&D money into so

### Statistics Problem Set: Frequency Distribution

Problem 1. Use the following data set. The data set represents incomes (in thousands of dollars) of 20 employees at an engineering firm. 50, 48, 46, 59, 44, 43, 35, 59, 48, 53, 46, 59, 52, 48, 51, 59, 53, 51, 53, 52 (a) Find the range, mean, median, and mode of the data set. (b) Make a frequency distribution for the data se

### Calculating Probabilities of a Dice Game

Suppose someone gives you 9 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win \$9.00 if you succeed and you lose \$2.00 if you fail. What is the expected value of this game to you? Should you expect to win or loose the expected value in the first game? What can you expect if you pla

### Probability Problems: Colored Candy Example

Use the theoretical method to determine the probability of the given outcome or event. A bag contains 5 red candies, 15 blue candies, and 20 yellow candies. What is the probability of drawing a red candy? a blue candy? A yellow candy? Something besides a yellow candy? The probability of drawing a red candy is ______ (round t

### Expected Value: Lottery

A magazine ran a sweepstakes in which prices were (see list below). listed along with the chance of winning. values 1 chance out of \$1,000,000 ; 80,000,000 \$100,000 ; 120,000,000

### Die throw problem

We repeatedly throw a die, stopping when the value of the throw exceeds the value of the first throw. Compute the expectation value of the number of throws.

### Binomial and Poisson Distributions in Real Life

Examples of the binomial and Poisson distributions are all around us. - Identify a real-life example or application of either the binomial or poisson distribution. - Specify how the conditions for that distribution are met. - Suggest reasonable values for n and p (binomial) or mu (poisson) for your example. -

### Poisson distribution

Q1: A sample of n independent observations x1, x2, . . . , xn are obtained of a random variable having a Poisson distribution with mean ?. Show that the maximum likelihood estimate of ? is the sample mean [see the attached file]. Show that corresponding estimator (X) is an unbiased estimator of ?, and has variance ?/n.

### Solving Probability Problems

Assume that the average number of traffic accidents requiring medical assistance between 7 and 8 AM on Wednesday mornings is 1. What then is the chance that there will be a need for exactly 2 ambulances during that time slot on any given Wednesday morning?