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# Probability

### Step by step calculations for probability

An airline is trying to determine whether the price of fuel will rise or fall in the future. They believe there is a 65% chance that the cost of fuel will fall. However, they are risk-averse and prefer to hire an analyst. The airline execs have found that when the price of fuel fell, the analyst correctly predicted the decrease

### Steady-State Distribution from a forward Fokker-Planck equation.

Question on obtaining the Steady-State Distribution for a Transition Probability Density Function from a forward Fokker-Planck equation. An example of a similar solution has been provided. Basically I need to show detailed workings from my forward equation to the steady-state probability distribution. Please answer as clearly as

### Probability an Alternator will Fail

A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a)both will fail? (b)Neither will fail? (c)One of the other will fail? Show all steps carefully.

### EMV Machine Purchase Combinations

6. The manager of an ice cream parlor located in a small resort town is trying to decide whether or not to purchase a new soft serve machine. The new equipment will cost \$3,200 or \$3.2k. The profitability of this investment will depend on whether the vacation season is booming or slow. There is a 15% probability the vacation

### Probability - 1. The shape of data is another indicator. There are four shapes commonly observed: symmetric, positively skewed, negatively skewed, and bimodal. What measure of location can be influenced by skewness? ...

1. The shape of data is another indicator. There are four shapes commonly observed: symmetric, positively skewed, negatively skewed, and bimodal. What measure of location can be influenced by skewness? 2. The probability is a chance of occurrence of an outcome. Can the probability of occurrence of one outcome in an experimen

### Probability Distribution - 1. Gender selection: In a case study of the Microsoft gender ... 2. Life Insurance: The Teleltronic Company provided life insurance policies for its ... [See the attached Question Files.]

Determine whether a probability distribution is given. In those cases where a probability distribution is not described, identify the requirements that are not satisfied. In those cases where a probability distribution is described, find its mean and standard deviation. 1. Gender selection: In a case study of the Microsoft g

### Probability of buying a new book

Suppose that 30% of all students who have to buy a text for a particular course want a new copy, whereas the other 70% want used copy. Consider randomly selecting 25 purchasers. a). What are the mean value and standard deviation of the number who want a new copy of the book? b). What is the probability that the number who want

### probability of tomato seeds germinate

A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 25 seeds. a. What is the probability that exactly 20 germinate? b. What is the probability that 20 or more germinate? c. What is the probability that 24 or fewer germinate? d. What is the expected number of seeds that germinate?

### Discrete probability distribution: mean, standard deviation..

Using historical records, the personnel manager of a plant has determined the probability distribution of X, the number of employees absent per day. It is: x 0 1 2 3 4 5 6 7 P(x) 0.005 0.025 0.31 0.34 0.22 0.08 0.019 0.001 a. Find the following probabilities: P(2 &#8804; X &#8804;

### Probabilty Distribution and Histogram

Long-term history has shown that 65% of all elected offices in a rural county have been won by Republican candidates. This year there are 5 offices up for public election in the county Let r be the number of public offices won by Republicans. a) Find P(r) for r=0,1,2,3,4, and 5 b) Make a histogram for the r probability d

### Probability: Votes, the Bernoulli Process, and Volume Purchasers

1. A May, 2004 news report indicated that George Bush 74% overall approval rating among Republicans. 26% of all others disapprove. Assume that 45 percent of registered voters are Republican. If you select a registered voter at random and the voter approves of the President's performance, what are the chances that the voter is a

### Binomial distribution: US Space Shuttle redundant systems reliability: a. Find the probability that this shuttle component functions successfully if n = 2. b. Find the probability that this shuttle component functions successfully if n = 4.

Many vehicles used in space travel are constructed with redundant systems to protect the flight crew and their equipment. In other words, backup systems are included with many vehicle components so that if one or more systems fail, backup systems will assure the safe operation of the given component and thus the entire vehicle.

### Normal Distributions: purchase amounts by customers

Suppose it is known that the distribution purchase amounts by customers entering a popular retail store is approximately normal with mean \$25 and standard deviation \$8. a. What is the probability that a randomly selected customer spends less than \$35 at the store? b. What is the probability that a randomly selected custom

### Simulation of queuing systems

Consider the following continuously operational job shop. Inter arrival times of jobs are described as follows: Time between arrivals (hrs) probability 0 0.23 1 0.37 2 0.28

### In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects three different senators, what is the probability that they are all women? An article in USA Today stated that "Internal surveys paid for by directory assistance providers show that even the most accurate companies give out wrong numbers 15% of the time." Assume that you are testing such a provider by making 10 requests and also assume that the provider gives the wrong telephone number 15% of the time. Find the probability of getting at most, one wrong number. (Assume the Binomial distribution applies.)

In the 107th Congress, the Senate consists of 13 women and 87 men. If a lobbyist for the tobacco industry randomly selects three different senators, what is the probability that they are all women? An article in USA Today stated that "Internal surveys paid for by directory assistance providers show that even the most accurate

### Expected Value. z-scores and other statistics concepts

1. For a sample selected from a population with a mean of µ=50 and a standard deviation of &#963; = 10: a. What is the expected value of M and the standard error of M for a sample of n=4 scores? b. What is the expected value of M and the standard error of M for a sample of n = 25 scores? 2. A population has a mean of µ

### Binomial Probability for Students

An unprepared student takes a three-question, true/false quiz in which he guesses the answers to all three questions, so each answer is equally likely to be correct or wrong. a)(4)The student gets three answers wrong. b)(4)The student gets exactly two answers correct. c)(4)The student gets only the first answer correct.

### Suppose a certain test detects cancer among people ... [See the attached question File.]

Suppose a certain test detects cancer among people ... [See the attached question File.]

### If a= 0.05, what is the probability of making a Type I error? a.0 b.1/20 c. 19/20 d. 20/20

If a= 0.05, what is the probability of making a Type I error? a.0 b.1/20 c. 19/20 d. 20/20

### Salaries and normal distributions

Please help with the following probability problem. According to the American Federation of Teachers, the average salary of 1998 college graduates with a degree in accounting was \$33,702 (USA Today, June 18, 1999). Assume that the distribution of current salaries of recent graduates with a degree in accounting is skewed to t

### The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches.

The heights of women at a large university are approximately bell-shaped, with a mean of 65 inches and standard deviation of 2.5 inches. Use this information to answer the following questions: a) What is the probability that a randomly selected woman from this university is 67.5 inches or taller? b) What is the probability

### A person claims to have ESP (extrasensory perception). A coin is tossed 16 times, and each time the person is asked to predict in advance ...

A person claims to have ESP (extrasensory perception). A coin is tossed 16 times, and each time the person is asked to predict in advance whether the coin will land heads or tails. The person predicts correctly 75% of the time (i.e., on 12 tosses). What is the probability of being correct 12 or more times by pure guessing?

### Students' Commuting Time at CSN

Suppose that students' commuting time at CSN, represented by the variable X, has mean= 29 minutes and standard deviation = 9 minutes. There are 6000 students at CSN and we are about to take a random sample of 40 students. a) Can we know in advance what the mean commuting time for the students in the sample will be? b) Calcu

### Reorder Point/ Optimal Order/ Total Carrying Cost

The manager of a car wash receives pricing schedule (shown below) from the vendor who supplies soap- and a promise of a 25% shorter lead time for deliveries. Currently, lead time is 4 days. Annual usage of soap is 4500 gallons. The car wash is open 360 days a year. Ordering Costs is \$ 30 per order and annual holding costs are \$

### Joint Probability Distributions

Determine the value of c that makes the function f(x,y) = c(x+y) a joint probability density function over the range: x greater than 0 and less than 3 and x less than y less than x+2 a) P(X<1, Y<2) b) P(1<X<2) c) P(Y>1) d) P(X<2, Y<2) e) E(X) f) V(X) g) Marginal probability distribution of X h) Conditional probabilit

### Expectation and Variance of a Random Variable - Expectation and variance of a random variable Let X be a random variable with the following probability distribution: ... [See the attached Question File.]

Expectation and variance of a random variable Let X be a random variable with the following probability distribution: ... [See the attached Question File.]

### Joint Probability Distributions - The time between surface finish problems in a galvanizing process is exponentially distributed with a mean a 40 hours. A single plant operates three galvanizing lines that are assumed to operate independently. ...

The time between surface finish problems in a galvanizing process is exponentially distributed with a mean a 40 hours. A single plant operates three galvanizing lines that are assumed to operate independently. a) What is the probability that none of the lines experience a surface finish problems in 40 hours of operations? b

### Probability Distribution for Audits

Question 1. An audit conducted by the St. Aleanis Hospital has determined that 15% of all patient bills contain an error of one form or another. After spending considerable effort to improve the hospital's billing process, the administrators are convinced that things have improved. They believe that the new error rate is somewhe

### Probability based on Z score.

Amount of soft drink distributed into a cup has a mean of 7.6 oz and standard deviation of 0.4 oz. using what is given a) Estimate the probability that machine will overflow an 8oz cup b) Estimate the probability that it will not over flow 8 oz cup c) The machine has been loaded with 850 cups. how many of these do you expect

### Statistics - Probability Distribution and Mean Determination

Incubated time for black chicks is distributed with a mean of 21days and standard deviation of 1 day.using what is given, If 1000 eggs are being incubated how many chicks do we expect to hatch a) in 19-23 days, in 20 to 22 dayd b) in 21 days or fewer d) in 18 to 24 days assuming all eggs hatched. This is what is given:u-3(me