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# Probability

### 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.

### Basic Statistics

1. When two balanced dice are rolled, 36 equally likely outcomes are possible. Let X denote the smaller of the two numbers. If both dice come up with the same number, then X equals that common value. Find the probability distribution of X. Leave your probability in fraction form. a. x P(X=x) 1 5/18 2 2/9 3 1/6 4 1/9 5 1/18

### Base Level Statistics

4. Use the appropriate table of areas to find the specified area under the standard normal curve to find the area that lies between 0 and 3.01 a. 0.9987 b. 0.4987 c. 0.1217 d. 0.5013 5. Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that t

### Statistics questions....

This is a statistics question that I cannot get a handle on, so I would appreciate your help. Please show the work for future reference. Thank you very much. A study of Hub Furniture regarding the payment of invoices reveals the time from billing until payment is received follows the normal distribution. The mean time until

### The use of z-scores to determine probability

The instructions are typed exactly, word for word, from the text book. I am just as confused as you are, if not more. I wish I could give you more info, but that is all I have. The book is poorly written. The book has not covered Test Statistics yet, therefore that is not needed. The three chapters leading up to this assign

### Fault Tree Analysis

Assume the probability of a tire blowout is 0.102% per 50,000 miles of use and that a person travels 13,000 miles per year in a car. Assume that the probability of loss of control is 30% if the blowout occurs on the front tires and 15% for the rear tires. If control is lost, the probability is 50% of veering to the right and 50%

### Random Variables Problem Set

Please provide step by step solution with all work shown for the attached problem sets. It is important to see the steps required to solve the problems so I can understand the process for future problems: (see attachment) 1. A die is loaded so that the probability of any side showing is proportional to the number on that side

### Statistical Reasoning Questions

I need some help with these statistic problems, with step-by-step detailed answers for my understanding: Item 1 Two students are in the same mathematics class. On 14 out of 15 quizzes, student A has outscored student B by at least 10 points. Which of the following statements best describes this situation? Explain your reaso

### Binomial probabilities and sample probabilities

A normal population has a mean of 80.0 and a standard deviation of 14.0. Compute the probability of a value between 75.0 and 90.0. Compute the probability of a value 75.0 or less. Compute the probability of a value between 55.0 and 70.0. In a binomial situation n = 4 and p = .25. Determine the probabilities of the following e

### Provide an example of a couple of variables that we work with that could meet the binomial criteria above.

1) Classify events into success or failure 2) P(success) stay the same on each trial 3) Counting the number of successes 4) Discrete data 5) Independence Provide an example of a couple of variables that we work with that could meet the binomial criteria above.

### Assessing probabilities and converting to a similar scale

Stacy is considering inviting Ned to lunch for Valentines Day and would strongly prefer NOT to run into her ex-boyfriend Jim while having lunch with Ned. Knowing Jim's dining preferences quite well, she assesses the following probabilities for Jim eating at the various restaurants as (1) Sam's Pizza, 0.1 (2) Sy's Sandwiches, 0.2

### Probability and Statistics - Intervals

The problem is about Intervals based on a n normal population distribution. Please see the attached file for the problems. I need a solution that is detailed and with explanation. It would be very helpful to me. The final answers in my book are: a.(.888, .964) b.(.752, 1.100) c.(.634, 1.218)

### Probability

A survey in March, 1994 issue of Life magazine indicated that nine out of ten Americans pray frequently and earnestly. A poll is now taken of 1000 randomly selected Americans. Assuming the 1994 survey is still accurate, find the probability that at least 925 of those polled will indicate that they pray earnestly.

### Sample proportion

Suppose that 15% of all adults jog. An opinion poll asks a simple random sample of 500 adults if they jog. a) What is the sampling proportion in the sample who jog? b) According to the 68-95-99.7 rule what is the probability that the sample proportion who jog will be 11.8% or greater?

### Hypothesis testing of PCB capacitors

Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB wit

### Testing of a hypothesis based on a single sample

The 3 problems are from the topic "Test of Hypothesis Based on a Single Sample" of Probability and Statistic. I need assistance with these problems. Need to find out the correct solution and answers. 9. Two different companies have applied to provide cable television service in a certain region. Let p denote the proportion

### Probability

According to an article appearing in the Wall Street Journal, about 70% of all U.S. households have a cellular phone. suppose that you are conducting a survey of customer satisfaction regarding their cellular phone. If you called 11 households selected at random, what is the probability that: (a) every household has a cellul

### What is the probability that the employee is female? The complement of A is. Use two digit random numbers, start with random number 00 and determine the random number ranges for the data set given above. How many units can be sold at the \$10 price? What is the probability of getting an A on the paper? Complete the table to make this a valid probability distribution. Compute the variance. Compute the standard deviation. What decision should be made by the optimist? What decision should be made by the conservative? What decision should be made using minimax regret? Using these random numbers, simulate the drying time for 5 processes. Use a four period moving average to forecast attendance at baseball games.

18. Employees of a local company are classified according to gender and job type. The following table summarizes the number of people in each job category. Male (M) Female (F) Job Administrative (AD) 110 10 Salaried staff (SS)

### Statistics Questions

8. In Syed's town there are 11,303 Hindi speakers. In Rajiv's town there are 19,251 Hindi speakers. In Jon's town there are 1,092 Hindi speakers. For this situation, what is the variable under consideration? 9.The members of a board of directors have the following roles: president (P), vice president (V), secretary (S),

### Probability of rolled die, blood type and Hindi speakers

1. If two balanced die are rolled, the possible outcomes can be represented as follows: (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (1,2) (2,2) (3,2) (4,2) (5,2) (6,2) (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) (1,4) (2,4) (3,4) (4,4) (5,4) (6,4) (1,5) (2,5) (3,5) (4,5) (5,5) (6,5) (1,6) (2,6) (3,6) (4,6) (5,6) (6,6) Determine the p

Question 4: The Evergreen Fertilizer Company produces fertilizer. The company's fixed monthly cost is \$25,000, and its variable cost per pound of fertilizer is \$0.15. Evergreen sells the fertilizer for \$0.40 per pound. Determine the monthly break-even volume for the company. Question 12: If the Evergreen Fertilizer Com

### Joint and Marginal PDF's. Multivariate Transformations

I am having troubles with #2 part (b) in the attached document. In part (a) I found what I believe to be the joint distribution for the transformation. I am questioning my interval for T (domain) for this joint distribution however. To complete part (b) it will be necessary to take the integral of the joint in part (a) with resp

### Probability distribution table problems

I have finished part of the table but I need help with the last two rows and the problems listed below. I need help on how the problems are solved and the correct formulas or clear solutions. I really do want to understand how to get the correct answer to the problems listed in attachment.

### Probability

A sample of waterfall heights in Hawaii show that the average height is 261.5 feet with a standard deviation of 13.76 feet. What is the probability AND percent chance of randomly selecting a waterfall in Hawaii that has a height between 255.7 feet and 273.2 feet.

### Relative Dispersion & Probability

Part A) What is the relative dispersion for each group? Explain the relative dispersion difference between the two? Mean StdDev Group 1 78 15 Group 2 47 10 Group 1 - Trashcan wt in rural area Group 2 - Trashcan wt in city NOTE: Both sample

### Probability - Combination Types

1. Assume you have ten (10) very expensive, leather bound books (all different authors) and you want to display these books on your fireplace mantle, but you are unsure how you want to arrange the books (by author, by height, year published, value . . . ). How many different ways can you arrange the books? 2. Assume you re

### Quantitative Methods, Maximax and Maximin Conditions

(See attached file for full problem description) --- 5. A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each crop given the two

### Quantitative Methods: Management Science and Probability and Stats

Please refer to the attached ms word file. #1: The Willow Furniture Company produces tables. The fixed monthly cost of production is \$8,000, and the variable cost per table is \$65. The tables sell for \$180 a piece. a. For a monthly volume of 300 tables, determine the total cost, total revenue, and profit. b. Determin