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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

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

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

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

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.

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

Probability: Are employment and economic trend independent?

Consider the following two economic characteristics with two possible outcomes each: employment (increase, decrease) and economic trend (positive, negative). Let the probability of a decreasing employment be 0.6 and the probability of a positive economic trend 0.5. Further, assume that the probability of a decreasing employment


1. According to the empirical rule, if the data form a "bell-shaped" normal distribution, ________ percent of the observation will be contained within 1 (one) standard deviation around the arithmetic mean. 68.26 75.00 88.89 93.75 2. The probability that a new advertising campaign will i

Probability of Defective Items from a Sample

A carton of 6 batteries contains 2 that are defective and 4 that are good. If we select 3 batteries at random form this carton, what is the probability that the sample contains exactly 1 defective battery? a) 33.3% b) 50.0% c) 60.0%


Suppose that a telemarketer calls a random sample of 12 households in a community in the night that 80% of the households have someone at home. Find the probability that the person doing the calling finds someone at home in exactly 10 households. a) 10.0% b) 28.3% c) 80.0% Find the mean of the above distribution. a)

Loglinearand logit models

Find a loglinear model that describes this data well. Interpret associations then treating whether killed as the response, find an equivalent logit model. Interpret the effects. See attachment

General Statistics

13) We use the General Rule of Multiplication to combine A. Events that total more than 1.00. B. Events based on subjective probabilities C. Mutually exclusive events. D. Events that are not independent. 14) Which of the following is a correct statement about a probability? A. It may be greater than

Interpreting a Normal Distribiution of two different brands of soft drink

See attached file. You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands. (Hint: if an individ

Binomial Probability: Arrival of Northwest Airlines

Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is .90. We select four flights from yesterday for study. 1. What is the likelihood all four of the selected flights arrived within 15 minutes of the scheduled time? 2. What is the likelihood that none of the selected f

Standard deviation of probability distribution for temperature

Suppose the probability distribution for the high temp in Nevada on June 1 is normally distributed with a mean of 65 degrees. If a box plot was made it would have an IQR = 20 degrees. 1. What's the standard deviation of that probability distribution? I know the answer is 20 / 1.35 - where do you come up with the 1.35?

Probabilty that none watched any of the three sports last year

A survey of a group's viewing habits over the last year revealed the following information: 1. 28% watched gymnastics 2. 29% watched baseball 3. 19% watched soccer 4. 14% watched gymnastics and baseball 5. 12% watched baseball and soccer 6. 10% watched gymnastics and soccer 7. 8% watched all three sports Calcula

Statistics: Problems and Solutions

1.FREQUENCY DISTRIBUTION & DESCRIPTIVE STATISTICS: Open the CUMBA.xls file, which contains data from a random sample of 100 employees at Mock Company Inc. Create a Frequency Distribution of the YEARS OF EXPERIENCE for the employees using intervals of 0-4, 4-8, 8-12, 12-16 and 16-20. Also create the Descriptive Statistics for