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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

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

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


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

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 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

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

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.

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?

Probabillity and possible outcomes

How do you find the probability of numbers such as two people need to choose a number between let's say 1 and 5. I would need to find the probability that they choose the same number. The next problem is about possible outcomes. How do you find the outcomes for three numbers like 3 boats, 5 cars, 3 trains. I am stuck how to f

Hilton Inn Probability and Inventory Control for Overbooking

The Hilton Inn has decided to use good inventory control to decide how many customers to book to the hotel. The hotel has 100 rooms and Hilton Inn charges $120 per night per room. The number of no-shows has the following probability distribution: Number of no shows Probability 0 0.10 1

Probability of individual being unemployed & high school dropout

In a depressed rustbelt city in Michigan, a newspaper investigative team found that a large majority of the city's youth were unemployed. The team defined youth as any city resident between the ages of 16-21. Of the population aged 16-21 and not in college, 13.5% are unemployed, 29.05 % are high school dropouts, and 5.32% ar