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# Probability

### Decision Making and State of Nature

Allen Abbott has a wide-curving, uphill driveway leading to his garage. When ther is a heavy snow, Allen hires a local carpenter, who shovels snow on the side in teh winter, to shovel his driveway. The snow shoveler charges charges \$30 to shovel the driveway. Following is a probability distribution of the number of heavy snows e

### Discrete Probability Distributions

A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces: a. Exactly 5 will be defective? b. 5 or more will b

### Binomial Distribution Chart - Probability Tree

7. Construct a binomial distribution chart and table showing all of the outcomes if a woman would like to know all possible outcomes of having 3 children. Also show this using a probability tree diagram. a. What are the odds the second child is a boy? b. What are the odds she has all 3 boys?

### Binomial Probability: Being Late for Work

According to a recent survey 20% of people are late for work on any given day. You are a manager of a department of 18 people. Find the probability that: a. 3 will be late on a given day. b. 0 will be late on a given day. c. More than 1 person will be late on a given day d. 2 or fewer will be late on a given day

### Probability

A lottery involves drawing five white balls out of a drum with 55 balls and then drawing one red ball out of a drum with 42 red balls. You can buy a \$1 ticket and select five white numbers from (1-55 inclusive and one red number (from 1 - 42 inclusive). you win the lottery if you pick all five of the correct white balls and th

### Determining Probability: Car Example Problems

If 80% of all people between the ages of 30 and 50 drive a car, find these probabilities for a sample of 20 people in that age group: a. Exactly 18 drive a car. b. 16 or more drive a car. c. At most 15 drive a car.

### Texas Hold 'em poker, flush probability.

Suppose you are playing Texas Hold'em poker and you are dealt the ace of hearts and the ten of hearts. What is the probability that you make a flush with exactly three more hearts on the board by the river?

### Finding number of different passwords

How many different computer passwords are possible? a.If each password consists of 3 symbols and if the first one must be a number and the other 2 must be letters b.If each password consists of 3 symbols and if the first one must be a Letter and the other 2 must be Numbers c.Which one do you believe is more secure and w

### Probability word problem

4. At a swimwear store, the managers found that 16 women bought white bathing suits, 4 bought red suits, 3 bought blue suits, and 7 bought yellow suits. If a customer is selected at random, find the probability that she bought: a. A blue suit b. A yellow or a red suit c. A white or a yellow or a blue suit d. A

### Probability of Card Selection

3. When a card is selected from a deck, find the probability of getting: a. A club b. A face card or a heart c. A six and a spade d. A king e. A red card

### Probability of Getting a Job

The table below represents the results of a survey of 500 Households in Q1 2005: Current Economic conditions: GOOD FAIR BAD Jobs Are HARD To Get 25 145 70 Jobs Are EASY To Get 100 145 15 a. If a Household is chosen at random, what is the probability that it feels economic conditions are GOOD? b. If a Ho

### Finding the Probabilities of Problems

7. A manufacturing company has three factories: X, Y, and Z. The daily output of each is shown here. Factory X Factory Y Factory Z TVs 18 32 41 Stereos 56 40 13 If one item is selected at random, find these probabilities. a. It is a TV b. It was manufactured at Factory Y c. It was manufactured at factory X

### EOQ Model for the Bridgeport City

The Bridgeport city manager and the chief of police agreed on the size of the police force necessary for normal daily operations. However, they need assistance in determining the number of additional police officers needed to cover daily absences due to injuries, sickness, vacations, and personal leave. Records over the past thr

### Probability calculation using frequency approach .

2. Suppose 90% of kids who visit a doctor have a fever, and 20% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat? The probability is ______. 3. The percent distribution of live multiple-delivery births (three or more babies) in a particular year fo

### Probability based on binomial distribution for quality control data.

The quality control process at a manufacturing plant requires that each lot of finished units be sampled for defective items. Twenty units from each lot are inspected. If five or more defective units are found, the lot is rejected. If a lot is known to contain 10% defective items, what is the probability that the lot will be rej

### Probability and simulating files for promotion

Individually remove all four aces from a deck of playing cards. There will now be 24 red cards in the deck, that will represent "male" files, and 24 black cards that will represent "female" files. Alternatively, you may use 48 index cards, marking half with "M" and half with "F". Shuffle the cards at least seven times and then

### Statistics - Probability and Sample Distribution

Although most people believe breakfast is the most important meal of the day, 25% of adults skip breakfast (U.S. News & World Report, November 10, 1997). Assume the population proportion is p = .25, and pbar is the sample proportion of adults who skip breakfast based on a sample of 200 adults. a) Show the sampling distributio

### Poisson Distribution for Major Earthquakes

For a recent period of 100 years, there were 93 major earthquakes (at leat 6.0 on the Richter scale) in the world (based on data from the World Almanac and Book of facts). Assuming that the Poisson distribution is a suitable model, find the mean number of major earthquakes per year, then find the probability that the number of e

### Probability: A Study of College Football Games

A study of college football games shows that the number of holding penalties assessed has a mean of 2.3 penalties per game and a standard deviation of 1.1 penalties per game. What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.4 penalties per game

### Probability

An oil explorer orders seismic tests to determine whether oil is likely to be found in a certain drilling area. The seismic tests have a known reliability: when oil does exist in the testing area, the test will indicate so 90% of the time; when oil does not exist in the test area, 5% of the time the test will erroneously indica

### Finance questions

1) You are interested in investing, and are considering a portfolio comprised of the following two stocks. Their estimated returns under varying market conditions are provided: Condition Probability of condition Return on security A Return on security B Economy Sluggish 0.3 0.16 -0.05 Economy Normal 0.

### 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? 2) The probability is 1 in 4,000,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime?

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. The probability is 1 in 4,000,000

### Finding Probability of Beer Drinkers

On average, 40 percent of U.S. beer drinkers order light beer. (a) What is the probability that none of the next eight customers who order beer will order light beer? (b) That one customer will? (c) Two customers? (d) Few than three? (e) Construct the probability distribution, make a graph of its PDF, and describe its shape.

### Probability of Different Scenarios

1. A study of 200 advertising firms revealed their income after taxes: Income after Taxes Number of Firms Under \$1 million 102 \$1 million to \$20 million 61 \$20 million or mor

### Determining range, mean absolute deviation, standard deviation and variance

1. A social scientist for a children's advocacy organization has randomly selected 10 Saturday-mornings television cartoon shows and carried out a content analysis in which he counts the number of incidents of verbal or physical violence in each. For 10 cartoons examined the counts were as follows: 27, 12, 16, 22, 15, 30, 14, 30

### Probability calculation for AIU job satisfaction data.

Using our data set from Unit 1, compose an email to the head of the American Intellectual Union which discusses the following: Be sure to include information about how you would use the concept of probabilities to apply to profiles for hiring more satisfied individuals. (Job Satisfaction is an attitude about one's job. It

### Calculation of probability for a binomial random variable

Suppose 1.5 percent of the antennas on new Nokia cell phones are defective. For a random sample of 200 antennas, find the probability that: None of the antennas is defective. Three or more of the antennas are defective.

### Probability of Defectiveness in Sample

A Tamiami shearing machine is producing 10 percent defective pieces, which is abnormally high. The quality control engineer has been checking the output by almost continuous sampling since the abnormal condition began. What is the probability that in a sample of 10 pieces: That exactly 5 will be defective? That 5 or more

### Calculate: The Probability of Completing an Assignment

Dr. Stallter has been teaching basic statistics for many years. She knows that 80 percent of the students will complete the assigned problems. She has also determined that among those who do their assignments, 90 percent will pass the course. Among those students who do not do their homework, 60 percent will pass. Mike Fishbaugh

### Probability

One-fourth of the residents of the Burning Ridge Estates leave their garage doors open when they are away from home. The local chief of police estimates that 5 percent of the garages with open doors will have something stolen, but only 1 percent of those closed will have something stolen. if a garage is robbed, wha