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# Probability

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### Binomial Probability: Women truck drivers

1. Five percent of American truck drivers are women. Suppose 10 truck drivers are selected randomly to be interviewed about quality of work conditions. A) Is the selection of the 10 drivers a binomial experiment? Explain the reasons for your answer. B) What is the probability that two of the drivers will be women? C) What

### Martin Manufacturing: Probability of defects in a sample

Martin Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspection procedure is to select 6 items, and if there are 0 or 1 defective cases in the group of 6, the process is said to be in control. If the number of defects is more than 1, the process is out of control. Suppose

### Probability Problem AK1: Application of students to more than one school

Use of TI - 83 plus calculator is permitted given that steps are provided. 1. An MBA new-matriculates survey provided the following data for 2018 students. Applied to more than one school Yes No 23 and under 207 201 24 - 26

### Draw a decision tree to determine the best solution for rezoning of a builder's land.

A builder has located a piece of property that she would like to buy and eventually build on. The land is currently zoned for four homes per acre, but she is planning to request new zoning. What she builds depends on approval of zoning requests and your analysis of this problem to advise her. With her input and your help, the de

### Model to optimize number of possible bids given budgets

The attached files provide a definition of the problem, especially the powerpoint slide. Given the information, I am trying to develop a linear programming model such that I maximize the number of possible bids given the limited resources of budgets and writers. Essentially, which of the 10 bids should I take on, given the

### Calculating Probabilities Using Z-values

7.12 A random sample is obtained from a population with a mean of 50 and a standard deviation of 12. A. For a sample of n = 4 scores, would a sample mean of M = 55 be considered an extreme value or is it a fairly typical sample mean? B. For a sample mean of n = 36, would a sample mean of M = 55 be considered an extre

### 6 Statistics Problems: Identify Probability Distributions

Identify Probability Distributions Determine whether or not a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability disbribution is not given, identify the requiremtns that are not satisfied. 10. Eye Color Groups of five babies are randomly sele

### Clinical psychologist and dreams: Sample points in experiments, probabilities

A clinical psychologist is given tapes of 20 subjects discussing their recent dreams. The psychologist is told that 10 are highanxiety individuals and 10 are low-anxiety individuals. The psychologist's task is to select the 10 high-anxiety subjects. a- Count the number of sample points for this experiment. b- Assuming tha

### Discrete Probability Distribution: game show for big money prizes

Discrete Probability Distribution ??? Imagine you are in a game show, where there are big money prizes that can be won. Now, let us start the money give-away! There are 4 prizes hidden on a game board with 16 spaces. One prize is worth \$4000, another is worth \$1500, and two are worth \$1000. But, wait!!! You are also

### Republican governor of a state with no income tax appointed a committee for changes

The Republican governor of a state with no income tax is appointing a committee of five members to consider changes in the income tax law. There are 15 state representatives--seven Democrats and eight Republicans--available for appointment to the committee. Assume that the governor selects the committee of five members randomly

### Calculation of Probabilities Using Charts

See attached file for the table. Carbon monoxide (CO) is a colorless, odorless, tasteless toxic gas produced by incomplete combustion in fuel-burning devices. Persons with CO poisoning often overlook the symptoms. In Ontario, a total of 981 cases of unintentional CO poisoning was reported. Each case was classified as fata

### Reliability with Independence: Probability of Failure in Engines

Please answer the question skipping no steps, show all symbols, equations, etc and give answer please. Q: Consider a 4 engine aircraft (2 on each wing) where the probability of an engine failure is 0.002 failures per year. Assume that the probability of 1 engine falling is independent of the behavior of the others. Determ

### Statistics: Z score, normal distribution, SAT scores, people selected for juries

See attached file. 1. For a population with a mean of µ=60 and a standard deviation of ?=24, find the z-score corresponding to each of the following samples. A. M=63 for a sample of n=16 scores B. M=63 for a sample of n=36 scores C. M=63 for a sample of n=64 scores 2. A population of scores forms a normal distribution

### Time to failure: binomial distribution

Please answer with all equations shown, solution and skip no steps please. Q1: Let N be a random variable with a binomial distribution with parameters (n,p). Find E(N) and var(N). Q2: A component with time to failure T has failure rate function: z(t)=kt for t>0 and k>0 a) Find the probability that the component s

### Statistics

1. How many ways can an EMT union committee of 5 be chosen from 25 EMTs? 100 125 15,504 53,130 2. Which of the following cannot be a probability? 0 -49 0.001 14% 3. List the sample space of rolling a 6 sided die. {1, 3, 5}

### Uniform Probability

A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 minutes and 40 minutes. What is the probability that the shopping time will be a. between 25 and 30 minutes? b. less than 35 minutes? c. What are the mean and standard deviatio

### Compute a System Reliability at 65%. How many components are required in parallel?

Problem: A system must have a reliability of 99%. How many components are required in parallel when each component has a reliability of 65%?

### System Reliability of 3 identical items in parallel; exponential function

Problem 1: Consider three identical items in parallel. What is the system reliability if each item has a reliability of 98%? Please explain why the exponential function is used for reliability.

### Statistics: Absences of blue-collar workers

4. In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. Martocchio a

### Example of calculation of the mean value and variance

The service life of an incandescent light bulbs used domestically was investigated. It was found that a light bulb can last up to 3 years, and the probability distribution of the number of years a light bulb was used before failure is given below: Years light bulb was used before failure (x) 0 1 2 3 P

### Binomial Probability of Child's Hair Color

The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have black hair ? (b) the probability that no more than 2 of their children have black hair ? (c) the probability that none of the children have black hair (d) wh

### Calculate conditional probabilities

• "29% of men admitted they had cheated" means that total at the bottom of the column labeled 'Male cheating' becomes .29 x 203 = 59 • "compared with 18.5% of women" implies this percent of females had cheated, or the total in the 'Female cheating' column is .185 x 203 = 38 Female cheating Female not cheating Total Ma

### Percent of price-to-earnings ratios for random companies

A financial advising company has determined that the price-to-earnings ratios for 20 randomly selected publicly traded companies range between 0.9 and 2.9. Given that the price-to-earnings ratios are uniformly distributed, answer the following questions. What percent of price-to-earnings ratios are between 1.90 and 2.48?

### Probability of Samples Containing Female Students

In a large university, 15% of the students are female. If a random sample of twenty students is selected, a. what is the probability that the sample contains exactly four female students? b. what is the probability that the sample will contain no female students? c. what is the probability that the sample will contain

### Statistics: Sun Love grapefruit production. How many were harvested this year?

Sun Love grapefruit growers have determined that the diameters of their grapefruits are normally distrubuted with a mean of 4.5 inches and a standard deviation of 0.3 inches. A) What is the probability that a randomly selected grapefruit will have a diameter of at least 4.14 inches? B) What percentage of the grapefruits has

### Determine the reliabilty of the five components

Please answer with each step to show how the problem was solved. Q1: A system consists of five identical components connected in parallel. Determine the reliability of the components such that the system reliabilty is 97%.

### String of christmas tree lights has 10 bulbs connected in series

Q1: A string of christmas tree lights has 10 bulbs connected in series. The identical bulbs are assumed to have independant life times with a constant failure rate lamda. Find lamda such that the probability that the string survives 3 weeks is at least 99%.

### Probability of 18-24 yr old consumers using VISA plastic cards in making purchases

Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic cards in making purchases. The results of the study provided the following probabilities. -The probability that a consumer uses plastic card when making a purchase is .37. -Given that the consumer uses a plastic card, there is a .19 probability

### Statistics: continuous probability distribution

I need some help with the following statistical concepts: Now we are going to talk about continuous probability distributions. In a continuous probability distribution, the variable can have a value within a range. The most common continuous distribution is the standard normal distribution, select a continuous random varia

### Probability based on Poisson distribution

It is estimated that 0.5 percent of the 1200 callers per day to the Customer Service Department of Dell, Inc. will receive a message that the line is busy and be automatically transferred to a winning mode until a "representative is available to talk to them." The distribution of call arrivals approximates a Poisson distribution