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Probability

Permutations: Different Ways the Winners Can Be Drawn

In the cash now lottery game there are 10 finalists who submitted entry tickets on time. From these 10 tickets, three grand prize winners will be drawn. The first prize is one million dollars, the second prize is one hundred thousands dollars, and the third prize is ten thousand dollars. Use the permutations rule to determine th

Compound events: Dice example

You roll two fair dice, a green one and a red one. a) Are the outcomes on the dice independent? b) Find P(1 on green die and 2 on red die). c) Find P (2 on green die and 1 on the red die). d) Find P(1 on green die and 2 on red die) or (2 on green die and 1 on red die).

Elementary Probability Theory: Botanist Example Problems

Elementary Probability Theory: A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant.To estimate the probability that a new plant will germination, a random sample of 3000 seeds was planted

Elementary Probability Theory: Rolling a Single Fair Die

a) If you roll a single fair die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely? b) Assign probabilities to the outcomes of the sample space of part? a)do the probabilities add up to 1 ? c) What is the probability of getting of getting a number less than

Exponential Distribution: Expected Value

The port of Trop can service only 1 ship at a time. However, there is mooring space for 3 more ships. Trop is a favorite port of call, but, if no mooring space is available the ships have to go to the next port. An average of 7 ships arrive each week, according to the Poisson process. The Port of Trop has the capacity to handle

Short Problems in Probability

1. A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is A) 5 B) 8 C) 15 D) 30 2.A certain system has two components. There are 10 different models of the first component and 10 different of the

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) what is the probability of a fatat accident over a lifetime? Explain your reasoning. Hint: Assume independent events. Why might the assumption of independence be violated? (b) why might a driver be tempted not to use a seat belt "just on this trip" ?

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) what is the probability of a fatat accident over a lifetime? Explain your reasoning. Hint: Assume independent events. Why might the assumption of independence be

Empirical rule

Weights of regular coke. Using sample data on the weights of coke, we find that the mean is 0.81682 lbs., the standard deviation is 0.00751 lbs, and the distribtution is approx. bell-shaped. Using the empirical rule, what is the approx percentage of cans of regular coke with weights between 0.80180 lbs. and 0.83184 lbs?

Determining Probability from a Summary Table

The following table summarizes results from the sinking of the Titanic: Men Women boys Girls Survived 332 318 29 27 Died 1360 104 35 18 If one of the Titanic passengers is randomly selected, find the probability of getting a woman or someone who didn't

Number of possible routes for airline service to 8 cities

You have just started own airline. You have one plane for a route connecting Austin, Boise, and Chicago. One route is Austin-Boise-Chicago and a second route is Chicago-Boise-Austin. How many different routes are possible if service is expanded to include a total of 8 cities?

Find a percentile from a known normal probability distribution

Please help with the following problem. A newspaper article reported that people spend a mean of 6 hours per day watching TV, with a standard deviation of 1.9 hours. A psychologist would like to conduct interviews with the 15% of the population who spend the most time watching TV. She assumes that the daily time people spe

Quantative Research Methods - 36. An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment. ... [Please the attached questions file.]

36. An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment. 39. A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The qual

Distribution for the Interest Rate: Home Loan

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). Interest Rate 7.0% 7.5% 8.0% 8.5% >8.5% Probability 0.12 0.23 0.24 0.35 0.06 If a bank is selected at random from the distribut

Probability Problem of Big Ten University

An alcohol awareness task force at Big-Ten university sampled 20 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained. Did Well on Midterm

Binomial Distribution

Use the binomial distribution to determine the probability that a student will get at least 8 out of 10 questions on a ten question multiple choice test correct by just guessing if each question has four choices. Assume that the student randomly guesses any of the four choices with a .25 chance of guessing the CORRECT choice.

Probability: Calculating the Odds

Question: If a person were to be hit by lightning, they have a 33 percent chance of being killed. (a) Find the odds that a person will be killed if struck by lightning. (b) Find the odds against a person being killed if struck by lightning.

1. In previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.84 inches ... 2. Use the Poisson distribution to find the indicated probabilities. In one year, there were 116 homicide deaths in Richmond, Virginia. For a randomly selected day, find the probability that the number of homicide deaths is 0. ... [See the attached questions file.]

1. In previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.84 inches. In a test sample of 40 new balls, the bounce heights had a mean of 92.67 inches and a standard deviation of 1.79 inches. Use a 0.05 significance level to determine whether there is sufficient evidence to sup

Probability of Thermometer Readings

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and a standard deviation of 1 degrees C. A thermometer is randomly selected and tested. Find the probability of a reading that is less than -2.75.

Probability

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and a standard deviation of 1 degrees C. A thermometer is randomly selected and tested. Find the probability of a reading that is between 2.00 and 2.34

Probability: Mean Weights of Men

Assume that mens weights are normally distributed with a population mean of 172 pounds and a population standard deviation of 29 pounds. If 81 men are randomly selected, find the probability that they have a mean weight between 100 and 165 pounds.

Probability - Scores for men on the verbal portion of the SAT

Scores for men on the verbal portion of the SAT test are normally distributed with a mean 509 and a standard deviation of 112. Randomly selected men are given the Columbia review course before taking the SAT test. Assume that the course has no effect. If 16 of the men are randomly selected, find the probability that their mea

Probability - The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. One classic use of the normal distribution is inspired by a letter to dear abby in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the US Navy. given this information, find the probability of a pregnancy lasting 308 days or longer.

The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. One classic use of the normal distribution is inspired by a letter to dear abby in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the US Navy. given this i

Probability - statistics for normally distributed I.Q.'s with mean

Please answer true or false and give reason why. 7. P (-0.5 < Z < -0.3) = 0.0736. 8. For normally distributed I.Q.'s with mean of 100 and standard deviation of 16, the probability that 25 randomly selected individuals have an average I.Q. less than 95 is 0.0594. 9. The standard error of a sampling distribution of means