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    Probability

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    Legitimate continuous probability distribution

    Assuming that the function below is a legitimate continuous probability distribution, find: P(X > 200) Hint: let u = x+100 (substitution rule) f(x) = 20000 / (x +100)^3 x > 0 0 elsewhere

    Probability of nonconforming apple juice containers on Machine I and II

    A well known apple juice production company maintains records concerning the number of unacceptable containers of apple juice obtained from the filling and capping machines. Based on past data, the probability that a container came from machine I and was nonconforming is 0.03 and the probability that a container came from machi

    Probability Problem: Horse race with 12 entries

    A horse race has 12 entries. Assuming that there are no ties, what is the probability that the three horses owned by one person finish first, second, and third? The answer in my book is .0045. Please show the workings.

    True or False Probability questions.

    1. (True or False) The six letters in the word CHEESE are rearranged in a random manner. The probability that it will still spell CHEESE is less than .5. 2. (True or False) In bridge(card game), it is more likely that North has no spades than that he has no aces. 3. (True or False) If three distinguishable balls are distri

    Probability of patient surviving from disease

    1. The probability that a patient recovers from a disease is 63%. What is the probability that: A) 2 out of 3 patients in a group with the disease will survive? B) Probability that all 3 will survive? Answers: Just show me how to get there. A) 44.1% B) 25% 2. There are 3 consulting firms that have the following

    Example Statistics Problems

    1. A study of a court system produced the following results: Note: G= guilty , G' = not guilty , J= judged guilty , J'= judged not guilty 80% of guilty (G) judged guilty (J) 93% of innocent (G') judged innocent (J') 5% innocent (G') judged guilty (J) 77% guilty (G) A) Find probability judged guilty (means find P(J

    Find the standard deviation of the distribution

    A marketing poll revealed that 45% of Americans say they that they have dinner regularly as a family. You randomly choose 10 American families and ask if they regularly have dinner together as a family. 1. Does this situation meet the binomial requirements? Why or why not? Address the four characteristics in the Key Points.

    Two-thirds of US households purchased ground coffee: annual expenditures

    In recent years, about two-thirds of US house holds purchased ground coffee. Consider the annual ground coffee expenditures for households purchasing ground coffee. assuming that these expenditures are approximately distributed as a normal random variable with a mean of $65.16 and a standard deviation of $10.00 A. find the pr

    Probability of Sample Proportion

    Cashier records from the last year show that 60% of all Grayson's Grocery store customers use a previously-obtained Grayson's discount card upon checkout. Management suspects the percentage of actual cardholders is higher because some customers may not use their Grayson's card during every visit They decide to sample random cust

    Sampling Distributions of diameter widths of steel rebar

    The population of diameter widths of steel rebar is normally distributed with a mean of 2.5cm and a standard deviation of 0.25cm. What is the probability that the average diameter width of a strip of rebar from a sample of 23 strips is more than 2.6cm wide?

    Employees who carry secondary health insurance

    Suppose that a large corporation surveys all of their employees, and finds that 24% of them carry secondary health insurance. A representative from GoldStar Care visits 100 employees, in hopes of selling about 76% of them secondary health insurance. Find the probability that at least 27 of them already carry secondary health ins

    Census: Joint Probability Distribution Table

    Please help with this problem: Using the data in the Excel file Census Education Data, construct a joint probability distribution for marital status and educational status. a. What is the probability that a person is divorced and has a bachelor's degree? b. What is the probability that someone known to have an advanced

    Probability: Fair Coin, Danville Population

    1. A fair coin is tossed 4 times. What is the probability that heads show up an even number of times (i.e., never, or twice, or all 4 times). 2. The population of Danville is 20,000. Can it be said with certainty that there must be two or more people in Danville with exactly the same three initials? 3. What is the total po

    Probability of Relocation to two Chinese Cities

    1. The probabilities of an American company will relocating to two Chinese cities are: P(Shanghai) = 0.65 P(Beijing) = 0.39 P(one or the other) = 0.77 What is the probability the company will locate to both cities at the same time(assuming it could have offices in both cities)? 2. Two cards are drawn in succession fro

    Calculate the Probability for a Silver Dollar Flipped Twice

    A silver dollar is flipped twice. Calculate the probability of each of the following occurring: a. a head on the first flip b. a tail on the second flip given that the first toss was a head c. two tails d. a tail on the first and a head on the second e. a tail on the first and a head on the second or a head on the first a

    Relation between exponential and beta distribution

    See attached file. Suppose that X_i has an exponential distribution with a parameter lamda_i > 0. How do a series of exponential distribution functions with distinctive pairwise of random variable X and lamda (ie X_1 and lamda_1, X_2 and lamda_2,..., X_n and lamda_n) be transformed into a beta distribution function? Note:

    Choices and Distinct Permutations: Example Questions

    a) Homes come in 3 designs and 5 heating systems, as well as the choice of a garage or carport. How many choices does that give? Is this simply the multiplication rule? b) How many distinct permutations can be made from the letters of the word 'Mississippi'?

    Probability Tree

    Problem 1: The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty-five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the prob

    Probability based on binomial distribution

    Angela works as a quality supervisor. She has uncovered a quality issue with safety brackets on baby swings. Angela determines that 21% of the safety brackets are out of spec. For a lot of 16 safety brackets, what is the probability that at most 2 of them will be defective? Express your answer as a decimal. Do not round

    Binomial Random Variable Application

    Rob works in quality at a well known saw blade company. An inspector on his team has uncovered an issue with the kerf dimension on the bandsaw blade line. Rob conducts a sampling study and finds that 7% of the bandsaw blades are out of spec. Unfortunately, a shipment of 25 bandsaw blades left the plant about 3 hours before t

    Probability: Colored Cards Example

    There are three cards. The first is green on both sides, the second is red on both sides and the third is green on one side and red on the other. We choose a card at random and we see one side (also at random). If the side we see is green, what is the probability that the other side is also green? Many people intuitively answer

    Selling Price of Stock: Atlanta Company Example

    Atlanta Company stock is expected to follow an exponential growth rate. The relationship between the current stock price P0, future price PT after time T, and the continuously compounded rate of return r, is: PT = P0erT. The stock does not pay any dividends and it sells for $55 a share. The continuously compounded expected retur

    Statistics: Listing the Elements of Spaces

    List the elements of each of the following sample spaces: A) S= { x | x^2 - x - 6 =0} B) The set of outcomes when a coin is tossed up 3 times or until one head appears C) The set S= { x | 2x - 4 >= 0 and x<1}

    Borrower Characteristics

    1. In examining borrower characteristics versus loan delinquency, a bank has collected the following information. 15% of borrowers who have been employed at their present job for less than 3 years are behind in their payments, 5% of the borrowers who have been employed at their present job for at least 3 years are behind in the

    Probability: Random Variable, Mean, Variance & Density Function

    Please see the attached file for properly formatted problem descriptions. (1) The random variable X takes on the values 0, 1,2,3 with respective probabilities 1 12 48 64 125' 125' 125' 125 (a) Find E(X),E(X2) and var (X) (b) Find E((3X ± 2)2 (hint: easy if you use the results in (a)) (2) A contractor's profit on a co

    Nash Equilibria

    The 31 members of the board of the Student S Inc. are about to take a secret ballot whether to accept the merger proposal of Student G. Corp. Each member can vote to accept the proposal, reject the proposal or to abstain. For the proposal to be accepted, 16 members must vote to accept it. All, the 31 members care about is being

    Binomial Probabilities Calculations Solving

    Answer the following: (A) Find the binomial probability P(x = 4), where n = 12 and p = 0.50. (B) Set up, without solving, the binomial probability P(x is at most 4) using probability notation. (C) How would you find the normal approximation to the binomial probability P(x = 4) in part A? Please show how you would calculate