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# Probability

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### Probability of less than 3 cancellations will occur for patients of mental health clinic

At an outpatient mental health clinic, appointment cancellations occur at a mean rate of 1.5 per day on a typical Wednesday. What is the probability that less than 3 cancellations will occur on two Wednesdays? A) 0.8089 B) 0.4232 C) 0.2510 D) 0.2240 E) 0.1255

### Calculating the Probability of Choice

Please help with the following problems. Abby, Deborah, Mei-Ling, Sam, and Roberto work in a firm's public relations office. Their employer must choose two of them to attend a conference in Paris. To be fair, the choice will be made by drawing two names from a hat. (This is an SRS of size 2) a) Write down all the possibl

### What is meant by a probability distribution? Use in the workplace.

What is meant by a probability distribution? Discuss how you could use one of the text probability distribution at your workplace to help solve a business problem. Illustrate an example by performing a probability distribution calculation.

### Probability models

In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate, that is, satisfies the rules of probability. Give specific reason for your answer. a) Roll a die and record the count of spots on the up-face: P (1) = 0 P (2) = 1/6 P

### Problems Involving the Rules of Probability

Although the rules of probability are just basic facts about percents or proportions, we need to be able to use the language of events and their probabilities. Choose an American at random. Define two events: A) = the person chosen is obese B) the person chosen is overweight, but not obese According to the National Cente

### Discrete probability model

Choose a person aged 19 to 25 years at random and ask, "how many times have you worked out in the past?" Call the response X for short. Based on a large sample survey, here is a probability model for the answer you will get: Days 0 1 2 3 4 5 6 7 Probability 0.68 0.05 0.07 0.08 0.05 0.04 0.01 0.02

### Binomial, normal distribution: Appeals panel judges, logging trucks, government bond

5.1 In a certain state, an appeals court consists of seven judges. For a routine case, three judges are chosen at random as a panel to hear a case and render a decision. How many distinct panels can be formed? 5.26 Logging trucks have a particular problem with tire failures due to blowouts, cuts, and large punctures; thes

### Probability Distribution: Operating a TrolleyLine

4.1 Among its various routes, a transit agency operates a trolley line. The line has a total of 18 trolley cars. Some of these cars are unavailable because they are being maintained or repaired. The probability distribution of Y = number of cars out of service on a randomly chosen day is given by the Excel spreadsheet in figu

### Density Function of Random Variables

The destiny function for a random variable X is given in terms of constant c.....

### Probability: Vehicle Type

Vehicle type Lower Class Middle Class Upper Class Total Toyota Sienna 3 53 71 127 Honda Odyssey 2 34 77 113 Dodge Grand Caravan 62 11 7 80 Total 67 98 155 320 A. If we select one person at random, what is the probability that person drives a Toyota Sienna? B. If we select one person at random, what is the p

### Probability - Geologist's Analysis of Grantie Specimen

A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite. The geologist instructs a laboratory assistant to randomly select 15 of the specimens for analysis. a. What is the PMF of the number of granite specimens selected for analysis? b. What is the probability that all specimens of one of the

### Statistics

Problem 2 Acme Tires manufactures two types of tires: high performance tires and all weather tires. 45% of the tires they produce are high performance tires. They offer a 40,000 mile warrantee on each of the tires they sell, and 89% of all tires exceed 40,000 miles of tread life. Furthermore, 37% of all the tires sold are both

### Probability that lifeline electricity usage is exceeded

A utility company offers a lifeline rate to any household whose electricity usage falls below 240 kWh during a particular month. Let A denote the event that a randomly selected household in a certain community does not exceed the lifeline usage during January, and let B be the analogous event for the month of July (A and B refer

### Difference: probability sampling and simple random

What is the difference between probability sampling and simple random sampling?

### Calculating and explaining the probabilities of smoking by race

5.74 Refer to the contingency table shown below. (a) Calculate each probability (i-vi) and explain in words what it means. i. P(S) ii. P(W) iii. P(S | W) iv. P(S | B) v. P(S and W) vi. P(N and B) Smoking by Race for Males Aged 18-24 Smoker

### Probabilities with Possible States of Nature

Suppose that you are given a decision situation with three possible state of nature: s1, s2, and s3. The prior probabilities are P(s1) =.1, P(s2) = .6, and P(s3) = .3. With sample information I, P(I|s1) =.15, P(I|s2) = .2, and P(I|s3) = .1. Compute P(s1|I) Compute P(s2|I) Compute P(s3|I)

### Computing binomial probabilities

Consider a binomial experiment with 2 trials and p = .3. For the following questions, round to the nearest hundredth. Compute the probability of 1 success f(1) Compute f(0) Compute f(2) Find the probability of at least 1 success What is the expected value? What is the variance? What is the standard d

### Probability - Defects - Poission Distribution - Windshields

A factory produces windshields for large commercial trucks. Assume a Poisson distribution; with an average of 4.8 defects per windshield: a. what is the probability that a windshield will have fewer than 6 defects? b. 7 or more defects?

### Probability of failure with redundant systems in aircraft engines

Modern aircraft engines are very reliable. One feature contributing to that reliability is the use of redundancy, where critical components are duplicated so that if one fails, the other will work. For example, single-engine aircraft now have two independent electrical systems so that if one electrical system fails, the other ca

### Expected premium cost of an insurance policy

A bonding company want to insure a construction projects completion. If the project is cancelled due to the contractor's lack of performance, the bonding company will cover the entire expenses of \$30,000, and it will pay only half of this amount if it is cancelled for any other reason. The bonding company assigns a probabi

### Failure of airplane alternators; bus riders with same birthday

1. A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully. 2. How many riders would there have t

### Statistics: Calculate probabilities in contingency tables

1. Refer to the contingency table below and calculate the following probabilities. Smoker Nonsmoker Row Total (S) (N) White (W) 290 560 850 Black (B) 30 120 150 Column Total 320 680 1000 a) P(S) b) P(W) c) P(S | W) d) P(S | B) e) P(S and

### TCO 1: Probability of more than 21 hours to make 1000 gallons of synthetic rubber?

(TCO 6) The time required to make 1000 gallons of synthetic rubber at a plant in South America in a recent year was normally distributed with a mean of 18 hours and a standard deviation of 2.5 hours. What is the probability that it will take more than 21 hours to make 1000 gallons of synthetic rubber? 1.2 0

### Probability Question: Synthesizing 100 Gallons Of Rubber

(TCO 6) The time required to make 1000 gallons of synthetic rubber at a plant in South America in a recent year was normally distributed with a mean of 18 hours and a standard deviation of 2.5 hours. What is the probability that it will take more than 21 hours to make 1000 gallons of synthetic rubber? 1.2 0

### Binomial probability: Introduction of Fast Care Unit

(TCO 5) A hospital is hoping to introduce a Fast Care Unit. The hospital claims that after the initial run, 87% of the patients were pleased with the service. We ask 20 randomly selected patients whether or not they are pleased with the service. (a) Is this a binomial experiment? Explain how you know. (b) Use the correct for

### Kroft Food Products: Decision tree analysis for a new line of salad dressings

Kroft Food Products is attempting to decide whether it should introduce a new line of salad dressing called Special choices. The company can test market the salad dressing in selected geographic areas or bypass the test market and introduce the product nationally. The cost of the test market is \$150,000. If the company conduc

### Probabilty & Conditional Probability: Insurance Claims

The following table gives the number of claims at a large insurance company by kind and geographical region. East South Midwest West Totals Hospitalization 102 98 39 62 301 Physician's Visit 263 514 120 351

### Probability: Height of Men Example

A survey was conducted to measure the height of men. In the survey respondents were grouped by age. In the 20-29 age group the heights were normally distributed with a mean of 67.9 inches and a standard deviation of 3.0 inches. A study participant is randomly selected. Find the probability that his height is less than 67 inches.

### Statistics: Probability, counting, discrete random variables, normal distribution

Please see the attached files.

### Probability of getting 9 correct answers

A True-False test has 20 questions with each having 2 possible answers with one correct. Assume a student randomly guesses the answer to every question. a. What is the probability of getting exactly 9 correct answers? b. What is the probability of getting less than 6 correct answers?