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# Probability

### 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

### Investment/maxium probability One of your friends has \$ 2000.00 available to invest. Assume that all the money must be placed in one of three investments; a money market fund, a stock, or gold. Each dollar that your friend invests in the money market fund earns a virtually guareanteed 12%. Each dollar that is invested in stock earns an annual return characterized by the probability distribution provided. Each dollar that is invested in gold earns an annual return characterized by the probability distribution provide. A) If your friend must place all the available funds in a single investment, which investment should he choose to maximize his expected earnings of the next year?

Please see the attached file(s). Problem One of your friends has \$ 2000.00 available to invest. Assume that all the money must be placed in one of three investments; a money market fund, a stock, or gold. Each dollar that your friend invests in the money market fund earns a virtually guareanteed 12%. Each dollar that is

### 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

### Probability

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 0.02. What is the probability that (a) both will fail (b) neither will fail (c) one or the other will fail ? Show all steps.

### 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?

### Binomial probability

Assume that a procedure yields binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial: n=6, x=2, p=0.45.

### Find the probability of event when working with a normal distribution

Assume that the readings on the thermometers are normally distributed with a mean of zero degrees and a standard deviation of 1 C. A thermometer is randomly selected and tested. Find the probability of a reading that is between -3.88 and 1.07.

### 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.

### Probability - If a bill is chosen at random what is the probability that it is either for the Midwest or from the South? Given the bill is from the east what is the probability that it is for a physicians visit? ... [See the attached questions file.]

Refer to table 3B. If a bill is chosen at random what is the probability that it is either for the Midwest or from the South? Given the bill is from the east what is the probability that it is for a physicians visit? ... [See the attached questions file.]

### Normal Probability Plots

Explain the use of normal probability plot to evaluate whether a set of data is normally distributed?

### 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, Variability, Regression and Statistical Measures

I'm stuck can you help me, please explain your answers. 1) The following payoff table shows profits associated with a set of 3 alternative under 2 possible states of nature. States A1 A2 A3 1 12 -2 8 2 4 10

### Probability - 1. 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 or the other will fail? Show all steps carefully. 2. The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime? Explain your reasoning carefully. 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"?

Question 1: 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 or the other will fail? Show all steps carefully. Question 2: The probabilit

### Probability Distributions - Using our data set from Unit 1, compose an email to the head of the American Intellectual Union which discusses the following: Begin your email to AIU by first providing an overview of the database, i.e. a story. ...

The problem: Using our data set from Unit 1, compose an email to the head of the American Intellectual Union which discusses the following: Begin your email to AIU by first providing an overview of the database, i.e. a story. Be sure to include information about how you would use the concept of probabilities to apply

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

### Find the probability of an adults IQ score.

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the probability that a randomly selected adult has a IQ between 110 and 120. Find the probability that a randomly selected adult has an IQ less than 135.