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Probability

Tree Diagram and Dice Tossing

Develop a tree diagram for tossing two, eight-sided gaming dice to figure out how many possibilities there are. Discuss the purpose of using such a visual in working out probability.

Payoff Table and Optimal Strategy in decision making.

The president of a large oil company must decide how to invest the company's $10 million of excess profit. He could invest the entire sum in solar energy research, or he could use the money to research better ways of processing coal so that it will burn more cleanly. His only other option is to put half of this R&D money into so

Statistics Problem Set: Frequency Distribution

Problem 1. Use the following data set. The data set represents incomes (in thousands of dollars) of 20 employees at an engineering firm. 50, 48, 46, 59, 44, 43, 35, 59, 48, 53, 46, 59, 52, 48, 51, 59, 53, 51, 53, 52 (a) Find the range, mean, median, and mode of the data set. (b) Make a frequency distribution for the data se

Calculating Probabilities of a Dice Game

Suppose someone gives you 9 to 2 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $9.00 if you succeed and you lose $2.00 if you fail. What is the expected value of this game to you? Should you expect to win or loose the expected value in the first game? What can you expect if you pla

Expected Value: Lottery

A magazine ran a sweepstakes in which prices were (see list below). listed along with the chance of winning. values 1 chance out of $1,000,000 ; 80,000,000 $100,000 ; 120,000,000

Die throw problem

We repeatedly throw a die, stopping when the value of the throw exceeds the value of the first throw. Compute the expectation value of the number of throws.

Binomial and Poisson Distributions in Real Life

Examples of the binomial and Poisson distributions are all around us. - Identify a real-life example or application of either the binomial or poisson distribution. - Specify how the conditions for that distribution are met. - Suggest reasonable values for n and p (binomial) or mu (poisson) for your example. -

Poisson distribution

Q1: A sample of n independent observations x1, x2, . . . , xn are obtained of a random variable having a Poisson distribution with mean ?. Show that the maximum likelihood estimate of ? is the sample mean [see the attached file]. Show that corresponding estimator (X) is an unbiased estimator of ?, and has variance ?/n.

Probability Concepts and the Standard Normal Distribution

Hi, I need some assistance with the following two questions. I am not sure that I understand the questions fully. Any assistance would be appreciated. 1. What are some conditions under which business decisions are made using probability concepts? Provide at least two examples of subjective probability. 2. What are the chara

Probability in Situations Given

A company that has 327 employees chooses a committee of 17 to represent employee retirement issues. When the committee was formed, none of the 83 minority employees were selected. 1. Find the number of ways 17 employees can be chosen from 327. 2. Find the number of ways 17 employees can be chosen from 244 non-minorities. 3. I

Mutually Exclusive events, Probabilities, and Binomial Distribution

1. Are the events mutually exclusive (Yes or No)? Event A: Randomly select a person between 18 and 24 years old. Event B: Randomly select a person that drives a convertible. 2. Decide if the events are mutually exclusive. Event A: Randomly select a person who uses email. Event B: Randomly select a person that uses social

Questions of Algebra dealing with probability, etc.

1. True or False? 1.08 is a valid value for the correlation coefficient, r. 2. True or False? -0.835 is a valid value for the correlation coefficient, r. 3. Using the scatter plot below, determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables.

Statistical Probability: Emergency Call Rates

1. Let sample mean = 70 and the sample variance = 36 and assume the data is normally distributed. Use ths information to answer the following: a. what is the median of this data set? b. find an interval that would contain 68% of all data values from the sample. c. find the x-value that corresponds to the 16th percentile d.

Life Tables

What are life expectancy tables and why are they important for life insurance companies?

Classical and Empirical Probability - Coin Tossing

1. Describe two main differences between classical and empirical probabilities. Gather coins you find around your home or in your pocket or purse. You will need an even number of coins (any denomination) between 16 and 30. You do not need more than that. Put all of the coins in a small bag or container big enough to allow th

Probability and Geometry: Writing the Correct Equation

1. Center (-8, 1), radius square root of 3. Write the correct equation. 2. 6x+7y=11 The equation in slope intercept Form is y = _______ The slope is _______ Y intercept is ________ 3. Two round fountains are similar. One measures 6'4" across and the other measures 8"7" across. The scale factor of the fountains is ___

Finite problems

7. Use the table to find the probabilities that a person's total charges during the period are the following: What is the probability that a person total charges are $1000 or more?___________ (type an integer or decimal group or 2 decimal places as needed) Chart shows probability of a person accumulating specific amounts of c

Pre-Calculus Questions

1) Jack and Jill ran a 200 meter race. Jill ran the race in 25 seconds and won by 5 meters; that is Jack had run only 195 meters when Jill crossed the finish line. They decide to race again, but this time Jill starts 5 meters behind the starting line. Assuming that both runners run at the same pace as before, who will win the se

Probability

I have completed some of the question. I need help with the formulas on how to solve the problems along with making sure what I have done is correct. 5.2 Textbook p 282 Exercises 22, 24, 32 A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleist's, 8 Maxflis, and 3 Top Flites, find the pro

The answer to Normal distribution problems

1. If the random variable z is the standard normal score and a > 0, is it true that P(z > -a) = P(z < a)? Why or why not? 2. Given a binomial distribution with n = 20 and p = 0.26, would the normal distribution provide a reasonable approximation? Why or why not? 3. Find the area under the standard normal curve for the foll

State Lottery and Coin Toss

Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from 4 hidden windows. Behind each is one of the following: $150,000, $200,000 $1 million, or a "stopper". Before beginning, the contestant is offered $100,000 to stop. Mathemati

Managerial Business

A couple has agreed to attend a "Casino Night" as part of a fundraiser for the local hospital. They do not like to gamble because they believe that gambling is generally a losing proposition. However, for the sake of the charity, they have decided to attend and spend $300 on the games. There will be four games, each involving st

Queuing Theory

The manager of the Radford Credit Union(RCU) wants to determine how many part-time tellers to employ to cover the peak demand time in its lobby from 11:00 am to 2:00 pm. RCU currently has three full-time tellers that handle the demand during the rest of the day, but during this peak demand time, customers have been complaining t

math5

About 30% of adults in United States have college degree. (probability that person has college degree is p = 0.30). If N adults are randomly selected, find probabilities that 1) exactly X out of selected N adults have college degree 2) less than X out of selected N adults have college degree 3) greater than X out of sel

Calendar orders

The J&B Card Shop sells calendars depicting a different Colonial scene each month. The once-a-year order for each year's calendar arrives in September. From past experience, the September to July demand for the calendars can be approximated by a normal probability distribution with r=500 and o=120. The calendars cost $1.50 each,

Queuing and Birth Death process problem: Operation Research Management

Q1) During the year 2000, there was an average of .022 car accident per person in the United States. Using your knowledge of the Poisson random variable, explain the truthin the statement, "Most drivers are better than average." Q2) My home uses two light bulbs. On average, a light bulb lasts for 22 days (exponentially distrib

Probabilities

1. This problem is in reference to students who may or may not take advantage of the opportunities provided in QMB such as homework. Some of the students pass the course, and some of them do not pass. Research indicates that 40% of the students do the assigned homework. Of the students who do homework, there is an 80% chance the

Probability when throwing five six-sided dice

Please help with the following problem. Compute the probabilities for each of the following when you throw five six-handed dice. 1) What is the probability that all five have different numbers? 2) What is the probability that at least four are the same? 3) What is the probability that exactly three are sixes?

Probability and computing the odds

Compute the odds of each of the following events and rank them in order of decreasing likelihood. 1) picking the right lottery numbers(5 different numbers between 1 and 59) plus the right "power ball" (a number between 1 and 39). **The 5 numbers between 1 and 59 do NOT need to be chosen in the correct order. What impact does