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Probability: Detecting an Income Missile

Assume that a single radar unit used to detect incoming missiles has a probability of 0.90 of correctly detecting an incoming missile attack. Furthermore, assume that four such individual and identical radar units (each with an individual probability of 0.90 of detecting an incoming missile attack) are used to create a radar ins

Uniform Distribution and Probability

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes. a. What is the probability that a guitar neck can be carved between 95 and 165 minutes? b. What is the probability that the guitar neck can be carved between 120 and 200 minutes? c. Determine the expected completion time for

Probability and Real World Probability

There are 2 types of probability: empirical and theoretical (classical). - Define the 2 probability types in your own words. - List 1 profession example for each probability type: empirical probability and theoretical (classical) probability. Explain clearly how these probabilities are used. - List a real-world probability

Poisson Distribution Probability Problem

During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. [Hint: It is a Poisson Distribution Problem.] a) What is the expected number of calls per hour? b) What is the probability of three calls in five minutes? c) What is the proba

Develop Probability Distribution

A technician services machines as companies in the Phoenix area. Depending on the type of malfunction, the service call can take exactly 1, 2, 3, or 4 hours. The different types of malfunctions occur at the same frequency. a. Develop a probability distribution for the duration of a service call. Duration of Call (x) f(x

Probabilities and Confidence

1. An important issue facing Americans is the large number of medical malpractice lawsuits and the expenses that they generate. In a study of 1228 randomly selected medical malpractice lawsuits, it is found that 856 of there were later dropped or dismissed (based on data from the Physician Insurers Association of America). a)

Calculating mean profit and probability using simulation

Develop a worksheet simulation for the following problem. The management of Madeira Manufacturing Company is considering the introduction of a new product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product is uniformly distributed between $16 and $24 per unit. The product will se

Quality Assurance and Binomial Distribution

John Rengel is the Quality Assurance Supervisor for Vino Supremo Vinyards. He knows that 10 percent of each box of corks is undersized. a) If he were to randomly select 120 corks from the next box, then how many of these corks would John expect to be undersized? b) If he were to randomly select 120 corks from each box,

Monte Carlo and Crystal Ball

1. Explain the difference between descriptive and prescriptive (optimization) models. 2. Describe how to use Excel data tables, scenario manager, and goal seek tools to analyze decision models. 3. Explain the purpose of Solver and what type of decision model it is used for. 4. What approaches can you use to incorporate uncert

Statistics Problem Set: Uniform and Exponential Distribution

86. Give the z-score for a measurement from a normal distribution for the following: a. 1 standard deviation above the mean b. 1 standard deviation below the mean c. equal to the mean d. 2.5 standard deviations below the mean e. 3 standard deviations above the mean 118. Suppose x is a binomial random vari

Statistics Problem Set: Binomial Random Variables

38. Suppose x is a binomial random variable with n = 3 and p = 3 a. calculate the value of p(x), x = 0,1,2,3 using the formula for a binomial probability distribution b. using your answers to part a, give the probability distribution for x in tabular form 42. The binomial probability distribution is a family of proba

Distribution and Security Analysis

2. Security analysts are professionals who devote full time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables? a. the closing price of a particular stock on the New york stock exc

Multiplicative Rule and Independent Events

48. For two events, A and B, P(A) = 0.4, P(B) = 0.2, and P(A/B)=0.6 a. find P(A and B) b. find P(B/A) 50. An experiment results in one of three mutually exclusive events, A,B, or C. It is known that P(A) =.30, P(B) = .55 and P (C) = .15. Find each of the following probabilities: a. P(A U B)

Exponential Distribution Function and Derivation of the Equation

Let F(t) = 1- e ^(- lamda*t) a) Show how to generate a random variable from the exponential distribution function shown above. Show derivation of the equation. b) Generate 10000 random variables X and Y with cumulative distribution F(t); do this twice using lambda =2,3 (so 2 columns of 10000 numbers each). c) Using the equa

Probability of selection from a group

We have 7 boys and 3 girls in our church choir. There is an upcoming concert in the local town hall. Unfortunately, we can only have 5 youths in this performance. This performance team of 5 has to be picked randomly from the crew of 7 boys and 3 girls. a. What is the probability that all 3 girls are picked in this team of 5?

Find Expected Results and Probability

1. If the IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. (a) Find the probability that a randomly selected person has an IQ score between 88 and 112. (Show work) (b) If 100 people are randomly selected, find the probability that their mean IQ score is greater than 103. (Show work) 2.

Outcomes of Variables

1. The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The probabilities associated with each of the six possible outcome pairs are given in the accompanying two-way table. Low Medium High

Probability with Dice.

Two fair dice are tossed, and the face on each die is observed. a. Use a tree diagram to find the 36 sample points contained in the same space. b. Assign probabilities to the sample points in part a. c. Find the probability of each of the following events: A = {3 showing on each die} B = {sum of two numbers showing

Probability Analysis for Quality Measurements

A company that crafts home and garden features has collected some data from routine quality control studies on its mowers. The last 30 days' findings are attached as an Excel document to this post containing 200 sample weights of mower blades. They do their best to implement in-process quality checks to remain in control and man

Probability Concepts and Discussion

1. Define probability and explain its three perspectives. Provide an example of each. 2. Explain the concept of mutually exclusive events. How do you compute the probability P(A or B) when A and B are, and are not, mutually exclusive. 3. What is the standard error of the mean? How does it relate to the standard deviation of

Statistics - Finding Standard Deviation

** Please see the attached file for the complete problem description ** 15) According to the empirical rule, what percent of data should fall between +/1 stdev? +/-2 stdev? +/- 3 stdev? How does this compare to the a. Results for a random shape at 20 samples? b. Results for a random shape at 200 samples? c. Results for a

Simulation Modeling

I've attached an Excel template for this problem and it needs to be answered using this template. Every home football game for the past eight years at Eastern State University has been sold out. The revenues from ticket sales are significant, but the sale of food, beverages, and souvenirs has contributed greatly to the overa

Statistics and Probability Exercises

1. Of households in the United States, 18 million, or 17%, have three or more vehicles, as stated in USA Today (June 12, 2002), quoting the Census Bureau as the source. (a) If two U.S. households are randomly selected, find the probability that both will have three or more vehicles. (Give your answer correct to four decimal pla

Probability in Normal Distribution

1. A certain brand of electric stove has a length of life that is approximately normally distributed with a mean life of 15.7 years and a standard deviation of 4.2 years (Blaisdell, 1998). a. What percentage of stoves would we expect to last less than 13.5 years? b. What percentage of stoves would we expect to last betwee

Conditional Probability using a Chart

Attached is a table showing the prevalence of Alzheimer's disease. Suppose an unrelated 77 year old man, 76 year old woman, and 82 year old woman are selected from a community. 1. What is the probability that all three of these individuals have Alzheimer's disease? 2. What is the probability that at least one of t

Some Japanese consumers are willing to pay premium prices for Maine lobsters

Some Japanese consumers are willing to pay premium prices for Maine lobsters. One factor in the high cost is the mortality rate during the long distance shipping from Maine to Japan. Suppose the number of deaths x per 10 lobsters is given by the following distribution. An air shipment of 750 crates, each containing 10 lobsters,

Queuing Theory Assignment

Winter Park Hotel Donna Shader, manager of the Winter Park Hotel, is considering how to restructure the front desk to reach an optimum level of staff efficiency and guest service. At present, the hotel has five clerks on duty, each with a separate waiting line, during the peak check-in time of 3:00 P.M. to 5:00 P.M. Observation

Sample Space for a Game

1. A standard deck of cards contain a total of 52 cards, 26 of which are red and 26 of which are black. A standard die has six sides that are equally likely to come up and are numbered from 1 to 6. A game is played where a single card is drawn from a standard deck and the color is recorded. A standard die is also rolled and the

Probability: EKA Manufacturing Company

1. EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit of part # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly cost of operating the production facility is $3000. How many units of part # 2206 have to be sold in a month to break-even? 2. A compa

Probability Calculation: Titanic Mortality Data

In this the anniversary of the sinking of the Titanic, it is interesting to look at the distribution of those who survived, and those who died. The table below describes the number of men, women and children who were passengers on the Titanic. The table lists both the number who survived as well as the number in each category wh