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# Probability

### 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}

### Binomial distributions: Probability that more than 5 bandsaw blades will be defective

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 the

### 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

### Average Number of Customers: Queuing Theory

People arrive at a restaurant at a rate of five per minute and wait to receive their order for an average of 5 mins. Customers eat in with a probability of 0.5 and carry out with a probability of 0.5. A meal requires an average of 20 minutes. What is the average number of customers in the restaurant?

### Binomial, Poisson, Normal Distribution; Confidence Intervals

See attached file. Binomial Distribution Determine whether or not the given procedure results in a binomial distribution. 1. Twenty different students are randomly selected from those attending a private boys school and asked whether he or she is traveling over the Christmas holidays. 2. A six-sided die is rolled

### Gender of Children, Birth Dates, Kentucky Lottery

See attached file. You may use a calculator on this assignment. Please show work where applicable as this will help me when assigning partial credit. Probability Questions 1. Find the probability of a couple having at least 1 girl among 7 children. Assume that boys and girls are equally likely and that the gender of a

### Statistics: Mike's Ice Cream mean sales; math aptitute test for college freshman

Part 2. Evaluate probabilities using the laws of probability, the standard normal distribution, t-distribution, or X2-distribution. Mike's Ice Cream shop sells ice cream and related products. Past experience indicates that the daily sales follow a probability distribution that has a mean of \$1000 and a standard deviation of \$

### Standard score for data value; probability of data value

A set of 50 data values has a mean of 45 and a variance of 9. I. Find the standard score (z) for a data value = 52. II. Find the probability of a data value < 52. III. Find the probability of a data value > 52.

### Selected employee has a technical job or is a soccer fan

See attached file. In a large corporation a sample of 136 employees have been classified according to the type of work and asked their preferred sport. The results are presented in the accompanying table. assume that one employee in this sample is selected at random. Find the indicated probabilities (express them as a decimal

### Conditional probability: LAN shutdown

The local area network (LAN) for the faculty of engineering computing system at the University of Waterloo is temporary shut down for repairs. Previous shut downs have been due to hardware failure, software failure or power failure. Maintenance engineers have determined that the probabilities of hardware, software and power prob

### Sampling in statistics and acceptance regions

Q1 - The probability of accepting a lot that is 10% defective is .677. Does that mean, then, that the probability of rejecting the lot is 0.333? Q2 - An acceptance sampling plan states that twenty 2-inch squares of the incoming material must be checked and if 3 or less squares are imperfect, the lot is accepted. What is the

### A tire company has developed a new type of tire: Probability analysis of miles

A Tire company has developed a new type of tire. Extensive testing shows that the number of miles the new tire will run before wearing out is normally distrubuted with a mean of 40,000 miles and a standard deviation of 4,000 miles (Hint: Sketch bell shaped curves for the three questions below. a) What is the probability that

### Azure Valley Electric average outage cost; TRP is offering ski chalet condos

1. Azure Valley Electric Co-operative has for many years contracted with a neighboring utility to handle emergency service requests which occur, primarily due to storm damage, at the average rate of 2 per hour. It now feels that it should probably assume this responsibility itself and has been presented with two proposals for v

### A nationwide real estate company claims average time to sell a home is 57 days

1. A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed. a. Assuming the company's claim is true, if one home is selected at random, what is the probability t

### Setting up a probability distribution

Fast Service Store has maintained daily sales records on the various size 'Cool Drink' sales. These are shown in the following table: 'Cool Drink' Price Number Sold \$0.25 75 \$0.35 120 \$0.50 125 \$0.75 50 a.Set up a probabili

### Statistics: Probability value, Probability distribution

See attached file for formulas. 2. Based on FAA estimates the average age of the fleets of the ten largest U.S. commercial passenger carriers is 13.4 years with a standard deviation of 1.7 years. Suppose that 40 airplanes were randomly selected from the fleets of these ten carriers and were inspected for cracks in the airplan