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# Probability

### Binomial Probability For Government Data

According to government data, the probability that an adult has never been in a museum is 15%. In a random survey of 10 adults, what is the probability that at least 8 visited a museum?

### Construct Confidence Intervals for Various Significances

Please help with the following: A polling company split a random sample in half and asked 477 respondents the question generally speaking, do you believe the death is applied fairly or unfairly in this country today? The pollesters asked the other 477 respondents the question, generally speaking do you believe the death penal

### Confidence Interval & Margin of Error

Please help with the following: 1. Of 515 Broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of bacteria that cause food borne illnesses 85% were infected with a particular bacterium. A) Construct a 90% confidence interval? The 90% confidence interval is from _

### Probability: Normal Distribution and the Central Limit Theorem

1. The weight of potato chips in a small size bag is stated to be 5 ounces. The amount that the packaging machine puts in these bags is believed to have a normal model with a mean of 5.1 ounces and a standard deviation of 0.08 ounces. a) What fraction of all bags sold are underweight? b) Some of the chips are sold in "bargain

### Mean (Average) And Standard Deviation Sample Calculation

The score distribution shown in the table is for all students who took a yearly AP stats exam. Score Percent of Students 5 13.3 2 21.9 3 24.9 2 17.8 1 22.1 Find the mean AND standard deviation:

### Finding the Mean and Standard Deviation Using Frequency Table

The score distribution shown in the table is for all students who took a yearly AP stats exam. Score Percent of Students 5 12.4 2 21.7 3 25.4 2 18.4 1 22.1 Find the mean AND standard deviation:

### A problem on geometric probability

Two persons, A and B, agree to meet at a place between 10 a.m to 11 a.m. The first one to arrive waits for 20 minutes and then leave. If the time of their arrival is independent and at random, what is the probability that A and B meet?

### 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

### Probability: Analysis of Variance

How would you explain the analysis of variance, assuming that your audience has not had a statistics class before?

### 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

### Consider the following two-person zero-sum game. Assume the two players have the same three strategy options.

Player B Player A Strategy b1 Strategy b2 Strategy b3 Strategy a1 1 3  -6 Strategy a2 2 -1 2 Strategy a3 2 7  -5 1. Is there an optimal pure strategy for this game? 2. If so, what is it? 3. Identify and eliminate dominated strategies an

### 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.

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