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Probability

Statistics Problem Set: Discrete Probability Distribution

4.182: For each of the following examples, decide whether x is a binomial random variable and explain your decision. (see examples attached). 4.184: Consider the discrete probability distribution shown here. x 10 12 18 20 p(x) .2 .3 .1 .4 a) Calculate mean, varian

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

Calculating the Mean and Variance of a Poisson Random Variable

1. Let X be a random variable with probability density function given by f(x) - 2(1 - x), 0 <= x <= 1, 0, otherwise a. Find the density function of Y - X^2 b. Find the mean and variance of Y. 2. Let X be a random variable with probability density distribution given by f(x) - x, 0 <= x <

Probability Exercises

1. Determine for the following box, whether number and shape are independent or dependent. The box has a triangle with a 3 in it, a square with a 2 in it, a square with a 3 in it, and a triangle with a 2 in it. a. dependent b. independent 2. There are 5 Democrats, 18 Republicans, and 14 Independents in a room. Two peopl

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?

Jar of Marbles Probability Questions for Stats Students

Two marbles are selected, one at a time from a jar of marbles containing 10 black, 10 brown, 10 white and 10 green marbles. Let x represent the number of white marbles selected in 2 separate selections from the jar. (A) If this experiment is completed without replacing the marbles each time, explain why x is not a binomial

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.

What is a Probability Distribution?

6. Determine whether each of the distributions given below represents a probability distribution. Justify your answer. (a) x 1 2 3 4 P(x) 1/4 1/12 1/3 1/6 (b) x 3 6 8 P(x) 0.2 2/5 0.3 (c) x 20 30 40 50 P(x) 3/10 -0.1 0.5 0.3

Finding probability and area under a distribution

1. Find the following probability for the standard normal random variables z P( -1.5< z < 1.5) 2. Find the area under the standard normal probability distribution between the following pairs of z- scores. A. Z= 0 and z= 3.00 B. z= 0 and z= 1.00 C. Z = 0 and z = 2.00 D. Z = 0 and z = 0.62 E. z = 0 and z = 0.39

Binomial and Empirical Probability

A baseball player hits 59 home runs during a season with 161 games. What is the empirical probability that the player would hit at least one home run during any given game of the season? On the basis of the answer how many home runs would we expect the player to hit during any stretch of 8 games during the season?

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

Normal Distribution and Probabilities

Given a normal distribution with a mean of 100 and a standard deviation of 10, if you select a sample of n = 25, what is the probability that the sample mean is a. less than 95? b. between 95 and 97.5? c. above ?102.2? d. There is a 65% chance that the sample mean is above what value?

Calculations of Probability

Calculate the following probabilities: a) Flipping "heads" with a normal coin five times in a row. b) Rolling a "6" with one die. c) Rolling a "7" with two dice. d) Drawing a jack OR a red card (with replacement). e) Drawing an ace, followed by a king (with replacement).

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

What is the probability that a flight is full?

A particular airline has 10:00 a.m. flights from San Francisco to New York, Atlanta, and Miami. The probabilities that each flight is full are 0.60, 0.40, and 0.50 respectively, and each flight is independent one another. a) What is the probability that all flights are full? b) What is the probability that only the New York f

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

Calculating Probability from a Distribution

11 Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed. The probability that the member selected at random is from the shaded area of the graph is___

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

Probability and Tree Diagrams

A manufacturer receives voltage regulators from the three different companies, A, B, and C. The proportions of the voltage regulators coming from the three companies are 65%, 27%, and 8%, respectively. If 90% of the voltage regulators are from A, 88% from B, and 70% of those from C meet the manufacturers expectations, what is th

Poisson distribution

A textile manufacturer estimates that it produces bolts of cloth with flaws following a Poisson distribution that has an average of one flaw per 200 feet of cloth. a. Find the probability that a given 200-foot length of cloth will have no flaws. b. What is the probability that there will be at least one flaw within a given 2

Probability Distribution for Population

Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed. The probability that the member selected at random is from the shaded area of the graph is ______

Statistical Analysis of Binomial Distributions

Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. N = 50, p = 0.5 The mean, µ, is ______ (round to nearest tenth as needed) The variance is ______ (round to nearest tenth as needed) The standard deviation is ______ (round to nearest tenth as needed)

Probability Distribution Analysis

The probability of an adverse reaction to a flu shot is 0.10. Let r be the number of people suffering a reaction from a flu shot that has been given to a group of 5 people. a. Find P(r) for r = 0, 1, 2, 3, 4, 5 b. What is the expected number of people that will have an adverse reaction to the shot? c. compute the standard d