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# Probability

### QUANTITATIVE METHODS

DYNACO MANUFACTURING COMPANY PRODUCES A PRODUCT IN A PROCESS CONSISTING OF OPERATIONS OF FIVE MACHINES. THE PROBABILITY DISTRIBUTION OF THE NUMBER OF MACHNES THAT WILL BREAK DOWN IN A WEEK FOLLOWS. MACHINES BREAKDOWNS PROBABILITY PER WEEK 0 .10 1

### Statistics: Monty Hall problem, draw three kings, urns of red & green balls, radial tires

1. The Monty Hall problem is as follows: A contestant on a game show is given the opportunity to select one of three curtains on stage. One curtain hides a valuable prize and the other two hide worthless prizes. After the contestants selection, Monty, who knows what is behind each curtain, draws back one of the remaining cur

### Poisson Distribution, probabilities, and Bernoulli trials

Please show all work. 1. Suppose that X has a Poisson distibution with parameter "lambda" = 3 Find P(X>0) 2. Suppose you toss ten coins and count the number of heads. What is the probability that the number of heads you count will lie within two standard deviations of the mean? 3. Consider a sequence of 600 Berno

### Probability of obtaining certain sample scores in a normal population

For a normal population with µ = 100 and &#963; = 20 find the following. (a) What is the probability of obtaining a sample mean greater than 110 for a sample of n = 4 scores? z = ____ p = ____ (b) What is the probability of obtaining a sample mean greater than 110 for a sample of n = 16 scores? z = ____ p = ____

### Probability of Winning 15 or More Prizes

Sponsors of a local charity decided to attract wealthy patrons to its \$500-a-plate dinner by allowing each patron to buy a set of 20 tickets for the gaming tables. The chance of winning a prize for each of the 20 plays is 50-50. If you bought 20 tickets, what is the chance of winning 15 or more prizes? A. 0.250 B. 0.021 C.

### Binomial Probability: High School Graduates Going to College

In a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 20 graduates selected at random, what is the probability that exactly 8 will go to college? A. 0.114 B. 0.887 C. 0.400 D. 0.231.

### Probability of a security system

40% of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: a. What is the probability all three of the selected homes have a security system? b. What is the probability none of the selected homes have a security system? c. What is the probability that at least one has

### Binomial Random Variable.

A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that 8 have relief within a few minutes? A. 0.001 B. 0.168 C. 0.667 D

### Probability of absenteeism

On a very hot summer day, 5 percent of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are abse

### Probability: Determining Number of Combinations

A combination lock has six settings, each containing numbers from 0 to 9. Determine: (a) how many different possible combinations exist for the lock. Identify (b) the probability of selecting (i.e., properly identifying) at random the combination of the lock on your first attempt. Finally, (c) now assuming that none of the

### Probability of events using a standard deck of playing cards

1. You possess a 'standard deck of playing cards' (n = 52). First, (a) identify the probability of selecting a spade, club, or heart. Second, (b) calculate the probability of selecting a spade, heart, diamond, or face card. Identify (c) the probability of selecting (in sequence) a two and a red jack (assuming that the fi

### Normal distribution: what is the probability of selecting a score greater than the mean?

For any normal distribution, what is the probability of selecting a score greater than the mean? A. 50% B. 25% C. 34.13% D. cannot be determined without additional information

### Probability computation

1. A real estate investor has two houses: A and B. Each house may increase in value, decrease in value, or remain unchanged. Consider the experiment of investing in the two houses and observing the change (if any) in value: a. How many experimental outcomes are possible? b. Show a tree diagram for the experiment.

### Probability mass function for positive difference

Let X be the positive difference between the scores obtained from two dice. a. find the probability mass function for X b. show that X follows a valid probability mass function c. Find P(X>=2) d. Find mu e. Find the variance [Hint: An example of a positive difference is |2-6|=4. So zero is considered a positive differen

### Random testing for defective components

A lot of 1000 components contains 300 that are defective. Two components are drawn at random and are tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Please refer to the attachment for the questions for this given scenario.

### Calculate probability of different outcomes conditional on favorable reviews

A manufacturing company is trying to decide whether to add a new product line and the marketing department has been asked to help with this decision. Information on previous products produced indicates that 10% are huge successes, 20% are modest successes, 40% break even, and 30% are losers. However before the product decision

### Application of Various Tools using Probability Theory

See the attached file. 1) The time it takes for a light bulb to burn out. Continuous The weight of a t-bone steak Continuous The number of people in class who have type B blood. Discrete 2) The mean (expected value) of the random variable is 3) The variance of the random variable is 4) The stand

### Probability distribution

Two cards are drawn without replacement from a pack X measures hearts drawn and Y measures clubs drawn, both are random variables. 1. What is the joint probaility mass function of x and y. Explain 2. What are the marginal probability mass functions of x and y.

### Odds of Two Persons Having Same Birthday

What are the odds that a longtime girlfriend and the woman that I marry will have the same birthday? The birthday is 7/22.

### Decision Trees and portfolio theory

Q1 A company has developed two types of synthetic fuel. However it has not developed efficient manufacturing processes for either of them. It has has the option to develop the manufacturing process for both, either or none of them. They estimate that if they try to develop a process for fuel A then their probability of success

### Statistics Questions

1.Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaine-induced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium (non-ED); survival time for people in both groups was at most 6 hours. The accompanying data comes fr

### 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 about the characteristics which may include the types of variables included, etc. Be sure to include informati

### Prepare and email with an overiew of the database

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 by first providing an overview of the database, i.e. a story about the characteristics which may include the types of variables included, etc. Be sure to include information about

### Probability & Mean Deviation

1. A card is drawn from a deck of 52 cards. What is the probability that it is an ace or a six? 2. The proability that a person has immunity to a particular disease is 0.3. Find the mean and standard deviation for the random variable x, the number of people who have immunity in samples of size 28. 3. The variable X is norm

### Conditional probability problems: What is the probability that a student who has failed the test came from the south district? What is the probability that a student from the entire school system, chosen at random, has passed?

1.) a metropolitan school system consists of two districts- north and south. the north district contains 60% of all students, and the south district contains 40% of all students. a minimum competency test was given to all students. 10% of the north district students failed, and 15% of the south district students failed. What

### Probability

A group of n people meet at lunch for a cup of coffee. They play a game to see who gets to pay for all the coffees. Each person flips a coin. If all the coins come up the same except for one person, then that one person gets to pay for all the coffee. If the coins do not result in this way, then everyone flips again until there

### Normal Probability: Lifetime of Participants in an Annuity Plan

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. A ran

### 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 by first providing an overview of the database, i.e. a story about the characteristics which may include the types of variables included, etc. Be sure to include information abou

### Probability Distributions

Refer to the Real Estate data, which reports information on homes sold in the Denver, Colorado, area last year. a. Create a probability distribution for the number of bedrooms. Compute the mean and the standard deviation of this distribution. b. Create a probability distribution for the number of bathrooms. Compute the mea

### Normal Probability and Z-score

Lab technicians at a major mdical lab can process an average of 400 blood samples a day with a standard deviation of 50 samples. The processing follows a normal distribution. Convert 445 blood samples into a z-value (standard score). What is the area under the normal curve between 400 and 482? What is the area under the nor