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    Probability

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    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

    Probability with Two Dice

    You roll two fair dice, a red one and green one a. what is the probability of getting a 4 on the red die and a 2 on the green die? b. what is the probability of getting a 4 on the red die or a 2 on the green die? c. suppose we know that a 4 was rolled on one of the dice. What is the conditional probability of that the s

    Statistics and Probability Exercises

    See the attached file. 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 cor

    Poisson Distribution in Queuing

    A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average s

    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,

    Poisson Distribution and Confidence Interval

    a) The mean number of cargo ships that arrive at a port is 3 per day. The port has staff and facilities to handle up to 6 ships in a day. Using the Poisson distribution, find the probability that, on a given day, i. five ships will arrive; ii. too many cargo ships will arrive. b) The following represents a random sample of

    Probability - Normal Distributions

    A credit union claims that the credit card debts carried by its clients are normally distributed with a mean of $3050 and a standard deviation of $950. a) What is the probability that a randomly selected client has a balance of less than $2900 on his credit card? b) The credit union wants to advertise some financial produ

    Probability Example Problems

    A student has to sit a multiple-choice test with fi ve questions. Each question has five answer choices. Only one of the choices is correct. He does not know what the answer is to any question, so he guesses the answer randomly. Find the probability of answering a) the fi rst question correctly; b) the first two questions

    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

    Probability Example Problem: Random Selection of Bulb

    A company just began manufacturing a new high-efficiency model of light bulb. A quality control engineer randomly selects 1500 of these bulbs from the most recent batch produced and tests them to be sure they work. Out of the 1500 tested, 29 would not turn on. Based on these results, what is the probability that a randomly selec

    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