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Probability

Probability Using a Frequency Table & the Central Limit Theorem

1. You roll a die, winning nothing if the number of spots is odd, $3 for a 2 or a 4 and a $18 for a 6. a) Find the expected value and standard deviation of your prospective winnings b) You play three times. Find the mean and standard deviation of your total winnings. c) You play 60 times. What is the probability that you wi

Computing a Payoff Table and Finding an Optimal Decision Using Given Data

Jim has been employed at Gold Key Realty at a salary of $2,000 per month during the past year. Because Jim is considered to be a top salesman, the manager of Gold Key is offering him one of three salary plans for the next year: (1) a 25% raise to $2,500 per month; (2) a base salary of $1,000 plus $600 per house sold; or, (3) a s

Examples of Independent and Dependent Variables

1) A company that sells different types of slippers wants to see how their new line of comfortable walking slippers sells so the company keeps changing the price on this certain product several times to find the best price for it. The company records the quantity it sells for each price level and then performs a linear reg

Basic Statistics: Mean, Standard Deviation, Probability, Normal Distribution

1) Adult American males have normally distributed heights with a mean of 5.8 feet and a standard deviation of 0.2 feet. What is the probability that a randomly chosen adult American male will have a height between 5.6 feet and 6.0 feet? A. 0.6826 B. 0.5000 C. 0.9544 D. 0.7500 2) A jar contains 12 red jelly beans, 20 yell

Regression & Residual Analysis

An experiment was carried out to assess the impact of the variables x1 = force(gm), X2 = power (mW), x3 = temperature (C) and x4 = time (msec) on y = ball bond shear strength (gm). The results are given in the problem 5 Excel data file. a. Perform a complete analysis. b. Perform a complete residual analysis. c. Check for col

X-bar and R-Chart

The dataset contained in the problem #4 Excel file gives data on moisture content for specimens of a certain type of fabric. a. Create an X-bar R chart, using the first 10 subgroups as the base period. Comment on what is shown. b. What did you assume to construct these control limits (be specific)? Check the assumptions.

steps on performing a 3-factor factorial design

1. An experiment was designed to see what factors affect the cleaning ability of a washing solution. Three factors were used in the experiment - the concentration of detergent, concentration of sodium carbonate, and concentration of sodium carboxymethyl cellulose. A larger value of the response indicates better cleaning abilit

Computing probability using the Rule of Addition

In our virtual world, we own a construction company and bid on projects. Based on our past history of winning bids on projects, the probability of winning the next contract to build a school is 0.40, to build a hospital is 0.30 and to build both a school and a hospital is 0.20. What is the probability of winning a contract to bu

History of Statistics

Describe the historical development of statistics and probability In non-Western cultures

Solving 3 Questions Relating to Power Model

1) A coworker is considering the use of a log linear (power) model using weight to estimate the cost of a missile engine. They have performed the following calculations in log space using natural logarithms. Select the corresponding unit space form of this power model equation. Log Space b1 = 1.109438 b0 = -0.122932 Cost

Calculating Probability With or Without Replacement

Two cards are drawn from single deck of 52 cards one after the other. - Find the probability of selecting a king from the first card. - If the first card is king and the card is not replaced, what is the probability of selecting a king from the second card? - Find the probability of selecting a king from the first card

Determining Independent or Dependent Events

Independent Events (I) or Dependent Events (D) 1) A spinner is flicked three times, and each outcome is recorded. _____ 2) One thousand numbered raffle tickets are sold. Three different items are raffled off by randomly selecting three different raffle tickets. _____ 3) A paper bag holds 4 slips of paper that are numb

Setting up likelihood function and finding MLE

Consider the following data from 50 Bernoulli Trials Let theta be the probability of the observing a one for any single trial. a) Find the likelihood of any sequence of s trials containing y ones. b) If the prior on theta is uniform such that p(theta)=1, find an expression for the posterior distribution for theta after 10 t

Statistical Testing for an Out-of-Control Process

A statistical process analyst is responsible for assuring statistical control. In one process, a machine is supposed to drop 11.4 ounces of mints into a bag. (Assume that this process can be approximated by a normal distribution). The acceptable ranges for weights of the bags of mints are 11.25 ounces to 11.55 ounces, inclusive.

Binomial Probability Distributions - Sample Surveys

Binomial probability distributions are used in business, science, engineering, and other fields. Suppose you work for a marketing agency and have to create a television ad for Brand A toothpaste. The toothpaste manufacturer claims that 40% of the toothpaste buyers prefer Brand A to Brand B. Your agency conducts a survey to check

Steps on calculating the hospital's cost of capital

Assuming you are the financial manager of a for-profit hospital, what is the hospital's cost of capital assuming that the hospital has the following capital structure on its Statement of Financial Position (SFP; also known as a Balance Sheet): Long-Term Debt: $300M; current Yield to Maturity (YtM) of 6.5%, selling at par.

Ipad Security Code

To log into an IPad, a four-digit security code needs to be typed. The code can be digits 0 through 9 or lower case letters a through z. How many four-digit codes can be formed in total? Is it likely that someone who is not the owner of the IPad will guess the code?

Linear Regression V1.0

The personnel director for a local manufacturing firm has received complaints from the employees in a certain shop regarding what they perceive to be inequities in the annual salary for employees who have similar performance ratings, years of service and relevant certifications. The personnel director believes that an employee'

Theoretical and Experimenatal Probability

Probability is an important topic, and students should be able to test theoretical computations against experimental data. Consider a deck of 52 cards with the following characteristics: 13 red cards, numbered 1 through 13 13 blue cards, numbered 1 through 13 13 green cards, numbered 1 through 13 13 black cards, numbered

Expectation of a mixture

A number N is chosen according to a Poisson distribution with mean 10. A fair coin is then tossed until N +1 heads are obtained. What is the expected number of tosses it will take to stop the experiment?

Random variable expectation, Polya urn

I need help in two probability problems using R program. Thanks so much! 1. Simulation of an expectation. Design a simulation exercise in R to approximate the value of E ( X^X) when X has a U [0,1] distribution. Plot the value of the approximation as the sample size goes from 1 to 10,000. Use the Notebook feature in RStudio

Solving various questions on fundemantals of statistics

12. Which of the following numbers could be the probability of an event? 1.5 , 1/2 , 3/4 , 2/3 , 0 , -1/4 34. For some diseases, such as sickle-cell anemia, an individual will get the disease only if he or she receives both recessive alleles. This is not always the case. For example, huntington's disease only requires on

Probability of a random sample

A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders. Suppose that this belief is correct. A random sample of 144 current stockholders is taken a. If random sample of 144 current stockholders is taken, what is th

Statistical Analysis of Simulation Results

" A company produces a product on a number of machines. Each machine generates between $200 and $400 of revenue per day according to the uniform probability distribution. When a machine breaks down, it must be repaired, and the repair time may take 1, 2, or 3 days to be completed according to the following probability di

Random Probability Distribution

Three marbles are chosen without replacement from a box containing 12 red, 7 blue, and 8 yellow marbles. Let X be the number of blue marbles chosen. a) Find and graph the probability distribution of X. b) Find the mean of the random variable X.

Probability of Twin Births

Based upon statistical studies it has been found that 3.32% of all births in the United States will result in twins being born. If 17,300 births are selected at random what is the probability that: a) at most 600 of them will result in twins being born? b) between 525 and 550 of them (inclusive) will result in twins being born

Probability: Selection Without Replacement

Suppose that you select 3 cards without replacement from an ordinary deck of playing cards. a) If the first card that you select is a spade and the second is a heart, what is the probability that the third card that you select is a spade? b) If the first card that you select is a four, what is the probability that the second

Probability - Department Stores (J C Penney, Macy's, and Sears)

A mall has three department stores, JC Penney, Macy's, and Sears. A survey of 2,118 people exiting the mall found that 433 made a purchase at JC Penney, 412 made a purchase at Macy's, 638 made a purchase at Sears, 109 made a purchase at JC Penney and Macy's, 167 made a purchase at JC Penney and Sears, 213 of them made a purchase