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# Probability

### 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

### Probability distribution table

The hospital keeps careful track of the number of emergency room visits and is particularly interested in tracking the number of patients during the summer months (historically the peak of the ER visits). Last summer ( a90-day period covering June-July-August), the number of patients seen is X The results are on the table belo

### Probability for a Ball Season

Bob Jones of the Alaskan Bears baseball club had the highest batting average in the 2000 Major League Baseball season. His average was .335. So assume the probability of getting a hit is .335 for each time he batted. In a particular game assume he batted three times. a. This is an example of what type of probability? b. Wh

### Normal Approximation of the Binomial

See the attached file. According to a recent census, 52.2% of New York residents are male. Suppose a group of 100 New York residents are selected at random. A) What is the mean and standard deviation of the number of male members of the group? B) Use the normal approximation to find the probability that less than half of th

### Statistics - Probability.

Probability : Suppose a fraction 5% of the circuits produced by a circuit manufacturer is defective. Historically, given that the circuit is defective, the inspector (wrongly) accepts the circuit 10% of the time, thinking that there is no defect. If a circuit is not defective, he always correctly ... (Please see attachment) Thi

### A Simpe Probability Problem

At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance?

### Normal Probability: Auto Repair Job

An auto repair shop takes an average of 45 minutes to complete a repair job. The owner of the shop has determined the repair time has a standard deviation of 7 minutes. A customer comes into the shop and states that she will return in 35 minutes -- at which time she must have the car ready to drive off. Using the normal probabil

### Probability/dependency

Age effects in medical care. The type of medical care a patient receives may vary with the age of the patient. A large study of women who had a breast lump investigated whether or not each woman received a mammogram and a biopsy when the lump was discovered. Here are some probabilities estimated by the study. The entries in the

### Probabilities

Refer to the Real Estate data (attached), which reports information on homes sold in the Denver, Colorado, are during the last year. a. Sort the data into a table that shows the number of homes that have a pool versus the number that don't have a pool in each of the five townships. In a home is selected at random, compute the

### General Statistics

1. The weekly salaries of teachers in one state are normally distributed with a mean of \$490 and a standard deviation of \$45. a. What is the probability that a randomly selected teacher earns more than \$525 per week? b. What is the probability a randomly selected teacher earns less than \$435 per week? 2. The i

### Probability of a sample proportion

A market research firm conducts telephone surveys with a 40% historic response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150/400=.375

### Financial advisor using Decision Tree

A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation: Investment Good Economy Fair economy Poor Economy Fund A \$10

### Statistics questions

1. The table below describes the smoking habits of a group of asthma sufferers. Nonsmoker Occasional Regular Heavy Total _________ Smoker Smoker Smoker_______ Men 424 39 72 36 571 Women 360 46 77 44 527_ Total 784 85 149 80 1098 a. If one of the people is randomly selected, find the probability of getti

### Probabilities, z scores and distributions

1. Two hundred raffle tickets are sold. Your friend has 5 people in her family who each bought two raffle tickets. What is the probability that someone from her family will win the raffle? 2. Answer the following: a. What does it mean to say that x = 152 has a standard score of +1.5? b. What does it mean to say that a

### Probability Exclusive Events

1. The events A and B are mutually exclusive. Suppose P(A) = .30 and P(B) = .20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen? 2. A study by the National Park Service revealed that 50% of vacationers going to the Rocky Mountain region visit Yellowstone Park, 4

### 5 Statistics Questions

1. Assume that 12 jurors are selected from a population in which 50% of the people are Mexican-Americans. The random variable X is the number of Mexican-Americans on the jury. X 0 1 2 3 4 5 6 7 8 9 10 11 12 P(x) 0.000 0.003 0.016 0.054 0.121 0.193 0.226 0.193 0.121 0.054 0.016 0.003 0.000 a. Find the probability of exac

### Discussion questions

1. This Discussion directs students to analyze a financial plan that realistically portrays a typical budgeting scheme. Students will calculate a mortgage payment and the effects of interest and financing on their budget. Last name ANG a. Select the first three letters of your last name. Each letter has a numerical pl

### Simple Statistics Problems (Entry Level)

4. For a population with &#956;=50 and &#963;=10. a. Find the z-score for each of the following X values. (Note: You should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.) X = 55 X = 60 X = 75 X = 45 X = 30 X = 35 b. Find the score (X

### Sampling Distribution

Problem 1: The mean television viewing time for Americans is 15 hours per week (Money, November 2003). Suppose a sample of 40 Americans is taken to further investigate viewing habits. Assume the population standard deviation for weekly viewing time is o = 3 hours. a. What is probability the sample mean will be within 1 h

### Binomial, Hypergeometric, and Poisson Distributions

Give an example for each of the following distributions, binomial, hypergeometric, and Poisson. Explain the differences and different characteristics.

### Random Samples

1. A Private firm reports that 8% of the 2 million small businesses who apply for loan each year receive special interest rate (usually higher than market rate) because of high riskiness associated with small business. Consider a random sample of 25 small businesses who have recently applied for the loan a. What is the probab

### Probability Statistics: 1. In a genetics experiment on peas, one sample of offspring contained... 2. With one method of a procedure called acceptance sampling ... 3. Evaluate the given expression and express the result using ... 4. Determine the written description of the complement ... 5. A "combination" lock is opened with the correct sequence of three numbers ... 6. A certain lottery is won by selecting the correct four numbers ... 7. The data in the following table summarizes blood groups and RH types ...

1. In a genetics experiment on peas, one sample of offspring contained 450 green peas and 1523 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of ¾ that was expected? The probability of getting a green pea is approximately

### Queuing Theory - Single-Channel Waiting Line Model

Marty's Barber Shop has one barber. Customers have an arrival rate of 5 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: a). What is the probability that no units are in the system? b). What is the probability that one customer is receiving a haircut and no one is wait

### Powerball Winning Combinations, Prizes, and Probabilities

Case Study: The Powerball 1. Review the case study on page 157 of the textbook. See other attachments 2. Recall that for a single ticket a player first selects five numbers from the numbers 1-55 and then chooses a Powerball number, which can be any number between 1 and 42. A ticket costs \$1. In the drawing five white balls are

### Statistical Analysis of 1000 Long Distance Telephone Calls

A statistical analysis of 1000 long distance telephone calls made from the headquarters of the Bricks and Clicks Computer Corporation indicates that the length of these calls is normally distributed with u=240 seconds and sigma = 40 seconds. a. What is the probability that a call lasted less than 180 seconds. b. What is the

### Probability of Customer Complaints

Suppose that four inspectors at a film factory are suppose to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages. Tom, who stamps 60% of the packages, fails to stamp the expiration date once in ever

### Statistics - Probability

A candy company distributes boxes of chocolates with a mixture of creams, toffees and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees and cordials vary from box to box. For a randomly selected box, let X = weight of creams and Y =weights of the toffees and the pdf

### Probability of union: Basic

Let B and C be two events such that P(B)=0.13 and P(C)=0.01 . (a) Determine P(B union C) , given that B and C are mutually exclusive . (b) Determine P(B union C) , given that B and C are independent . Do not round your responses. (a) = (b) =

### Probability of intersection or union: Word problems

WLD Incorporated, a national data-collection agency, estimates that 55% of all customers at home warehouse stores (in the United States) own their own home. WLD also estimates that 30% of all home warehouse customers have lived at their current address for less than five years, and that 58% of all home warehouse customers own th