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# Probability Theory

### Statistical Analysis and Probability Sample Questions

1. For a particular sample of 80 scores on a psychology exam, the following results were obtained: First quartile = 59 Third quartile = 90 Standard deviation = 10 Range = 57 Mean = 75 Median = 74 Mode = 41 Midrange = 69 Answer each of the following: I. What score was earned by more students than any other scor

### Chebyshev's Theorem for a Sample of Scores on a Psychology Exam

For a particular sample of 77 scores on a psychology exam, the following results were obtained. First quartile = 44 Third quartile = 71 Standard deviation = 6 Range = 45 Mean = 64 Median = 57 Mode = 92 Midrange = 60 I. What score was earned by more students than any other score? Why? II. What was the highest score

### Quartile, Percentile, Range, Mid-Range, Descriptive Statistics, Measures of Central Tendency, Chebyshev's Theorem, Empirical Rule, Scatter Plot, Correlation and Regression, Z-Score.

1. For a particular sample of 50 scores on a psychology exam, the following results were obtained. First quartile = 39 Third quartile = 71 Standard deviation = 10 Range = 62 Mean = 62 Median = 61 Mode = 68 Midrange = 69 Answer each of the following; show all work. - What score was earned by more students

### Statistics Theory True-or-False Questions

True or False? 1. Statistics is a tool for turning data into information for making decisions. 2. Counting and categorizing are basic forms of statistics. 3. The mean and the median are essentially the same measures and are interchangeable. 4. Samples with the same means always have the same standard deviations. 5. The c

### Probability Theory

1. There are two events A and B, both with nonzero probabilities. If the occurrence of B makes occurrence of A more likely, is it ALWAYS true that the occurrence of A also makes occurrence of B more likely? (hint: "B makes occurrence of A more likely" can be represented as "P(A&#9474;B) > P(A)") 2. A parking lot consists o

### Price of Gas, Hours of Student Study and UPS Box Weights

See the attached file for the full problems. 1. NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is \$1.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, WI, area revealed that the mean price was \$1.52 per gallon and that the

### Probability Theory

Given the Probability Axioms: Nonnegativity: P(A) &#61619; 0 for every event A Additivity: if all Ai are disjoint, then: P(A1 &#61640; A2&#61472;&#61640; ...) = P(A1) + P(A2) + ... Normalization: P(&#61527;) = 1 1. Let A and B be independent events with AC denoting the complement of A. Prove that AC is independent of B

### Chebyshev's Theorem: Example Problem

1. The lengths of pins produced by a machine follow a normal distribution with mean 2.54 cm and standard deviation 0.04 cm. A pin is rejected if its length is less than 2.44 cm or more than 2.60 cm. Find the percentage of pins that are accepted. 2. If it is decided that 2.5% of the pins are to be rejected because they are

### Probability Theory

In a sample of 1,000 representing a survey from the entire population, 650 people were from Laketown, and the rest of the people were from River City. Out of the sample, 19 people had some form of cancer. Thirteen of these people were from Laketown. Are the events of living in Laketown and having some sort of cancer independe

### Refer to the Baseball 2005 data, which reports information

Refer to the Baseball 2005 data, which reports information on the 30 major league teams for the 2005 baseball season. a. Select the variable team salary and find the mean, median, and the standard deviation. b. Select the variable that refers to the age the stadium was built. (Hint: Subtract the year in which the stadium was b

### Chebyshev's theorem

The mean elevation of the 75 highest mountains in the United States is 15000 feet with standard deviation 1390. Whats the interval containing at least 75 percent and 89 percent of these elevations?

### Basic Statistics

Part I T/F and Multiple Choice Questions 1. Each set of data has four quartiles; they divide the ranked data into four equal quarters. _____ (T/F) 2. For any distribution, the sum of the deviations from the mean equals zero. _____ (T/F) 3. In a data set, the mode will always be unique. _____ (T/F) 4. The mean, m

### Probability Theory with Coins, Dice and Cards

1. Suppose you have 2 nickels, 3 dimes, and 8 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that a. You will draw a dime? b. You will draw a nickel? c. You will draw a quarter? 2. You are rolling a pair of dice, one red and one green. What is the probability of the

### Probability and Statistics

Evaluate the permutation. 1) P( 9, 5) 1) _______ A) 9 B) 1 C) 504 D) 15,120 A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find the probability. 2) All cherry 2) _______ A) .7272 B) .3636 C) .1091 D) .1212 In a ce

### Discussion Question

Part A: What is dispersion? Briefly name five measures of dispersion. Describe the characteristics of the standard deviation. Explain! Part B: Briefly describe to what kind of data does Chebyshev's Theorem apply? To what kind of data does Empirical Rule apply? Explain.

### Mean, Median, Mode, Distributions and Standard Deviations

1) Customers waiting at Ellerton Bank have been complaining about the amount of time they must wait in line. Managers at the bank, beginning to investigate the problem, have recorded sample waiting times for customers at the bank. Here are the waiting times (in minutes): 11, 21, 17, 9, 12, 23, 7, 5. A) What is the median of

### Chebyshev's Theorem Discussed

Chebyshev's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is: a. 90% b. at least 90% c. 96% d.at least 96% e. 25%.

### Estimate Sample Size N with Chebyshev's Theorem

Suppose that a measurement has mean M and variance = 25. Let X bar be the average of n such independent measurements. Use Chebychev's inequality to estimate how large n should be such that P(|X bar - M | < 1) = 0.95.

### Means & probability

Means & probability The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of

### Means & Probability: Queuing Theory

Q1 In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour or 0.6 customer per minute. Use the exponential probability distribution to answer the following questions.

### Elementary probability theory - A sale representative must visit 4 cities: Omaha, Dallas, Wichita, and Oklahoma City. Use the multiplication rule of counting to determine the ...

A sale representative must visit 4 cities: Omaha, Dallas, Wichita, and Oklahoma City. Use the multiplication rule of counting to determine the number of different choices the sales representative has for the order in which to visit the cities.

### Measures of variation

Pax World Balanced: x with line over it= 9.58%;s= 14.05% Vanguard Balanced Index : x with line over it = 9.02%;s = 12.50% These are the means and standard deviations of annualized percent returns. A) compute the coefficient of variation for each fund. If x (with line over it)represents return and s represents risk, then exp

### Introduction to Statistics

Having trouble comprehending the attached questions. Need to complete these tasks for a study guide to final exam. 1 of 9 A medical research team studied the ages of patients who had strokes caused by stress. The ages of 34 patients who suffered stress strokes were as follows. Use 8 intervals starting with 25-29. 29 30 3

### The Dutch Book Argument of Probability

What is Dutch book argument for the first axiom of probability (the one that says that the probability of a sentence is never less than 0 or more than 1)? Anyone know that theory?

### Decision theory

See attached notes to solve for problems in the attachment. Show work. 3-17 Although Ken Brown is the principal owner of Brown Oil, his brother Bob is credited with making the company a financial success. Bob is vice president of finance. Bob attributes his success to his pessimistic attitude about business and the oil in

### Functions and Statistical Models

4.30 A team of consultants working for a large national supermarket chain based in the New York metropolitan area developed a statistical model for predicting the annual sales of potential new store locations. x 1 2 3 4 5 6 7 8 9 10 Relative Frequency .01 .04 .04 .08 .10 .15 .25 .20 .08 .05 a) Find E(x) and interpret its valu

### Three Types of Probability and Assumptions

Discuss the three types of probability and the three assumptions underlying the probability theory.

### Application of Chebyshev's theorem in probability calculation

BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean

### Calculation of probability based on Chebyshev's inequality.

1. According to Chebyshev's theorem, at least ________, of the lifetimes lie between 609.5 hrs and 1074.5 hrs. a. 56% b. 75% c. 84% d. 89% 2. According to Chebyshev's theorem, at least ________, of the lifetimes lie between 656 hrs and 1028 hrs. a. 56% b. 75% c. 84% d. 89% 3. Suppose that th

### Payoff Table/Decision Situation

The Loebuck Company must decide how many cases of milk to stock each week to meet demand. The probability distribution of demand during a week is shown in the following table. Each case costs the grocer \$10 and sells for \$12. Unsold cases are sold to a local farmer ( who mixes the milk with feed from livestock) for \$2 per case.