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# Probability

### Calculation of probability based on normal distribution.

The number of shark attacks per year in the US is distributed approximately normal, with a Variance of 31.8 and a standard deviation of 10. A) Determine the number of shark attacks per year that separate the top 2% from the bottom 98 % B) Determine the number of shark attacks per year that constitute the middle 80% of shar

### Stat Market Survey: Microsoft Windows as the Operating System

A survey conducted by Stat Market showed that 94% of computer users use Microsoft Windows as their operating system. Suppose 12 computers users are randomly selected. A) Find the probability that exactly 10 of them use Microsoft Windows B) Find the probability that 10 or more of them use Microsoft Windows C) Find the pr

### Analyze probability of guessing correct answers

While taking a multiple choice test, I realize I cannot answer the 5 questions without guessing. There are 5 choices for each question, A B C D or E. Only one answer is correct for each questions. What is the probability of me guessing. A) Exactly two correct B) At most two correct C) All Five Correct

### Probabilities of number of fish caught at a particular location on a river

At a particular location on a river the number of fish caught per man-hour of fishing effort has a Poisson distribution with ?= 1.3 fish per man hour. Find the following probabilities: a. That four fish will be caught by one man fishing 2 hours. b. That six fish will be caught by three men fishing 20 minutes each.

### Poisson distribution: Manuscript pages typing errors

In a lengthy manuscript, it is found that only 2/3 of the pages contain no typing errors. Assume that the number of errors per page has a Poisson distribution. a. Find the expected number of errors per page? b. What percentage of pages has exactly one error?

### Probability of rejecting a sample of a roll of carpet

An inspection plan is set up to to randomly sample 3ft^2 of a 1000 ft^2 carpet and to accept the carpet if no flaws are found in the 3 ft^2 sample. What is the probability that a roll of carpet with an average of 1 flaw per square foot will be rejected by the plan?

### Known mean population and an unknown variance

A normal population has a known mean 50 and unknown variance. a) A random sample of n=16 is selected from this population and the sample results are x-bar = 52 and s= 8. How unusual are these results? Explain. b) A random sample of n=30 is selected from this population and the sample results are x-bar = 52 and s=8. How unu

### Probability in coin tosses, fair die rolling

See attached file for complete problem set. 1. Find the probability of obtaining three heads. 2. What is the probability that he will be at his starting point after three flips of the quarter? 3. What is the expected number of 1's? 4. What is the standard deviation of the number of 2's?

### Discrete Probabilty Distributions for Lottery Payouts

The payouts of the lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is \$1.00. Find the mean and standard deviation. Hint: don't forget to include the cost of the ticket and its corresponding probability. Divisions Payout Odds

### Microsoft, Apple and Google, descriptive, correlation matrix

Date Google Close Microsoft Close Apple Close 31/12/2009 619.98 30.34 210.73 30/12/2009 622.73 30.82 211.64 29/12/2009 619.4 31.24 209.1 28/12/2009 622.87 31.02 211.61 24/12/2009 618.48 30.86 209.04 23/12/2009 611.68 30.78 202.1 22/12/2009 601.12 30.68 200.36 21/12/2009 598.68 30.38 198.23 18/12/2009 596.42 30.22 195.43

### How Much Time for Those Who Take the Examination

The time it takes to answer an examination for admission to a school in a random variable that is presumed normal. On average, answer it completely takes people 70 minutes, with a standard deviation of 12 minutes. Determine how much time should be given to those who take the examination for 90% of the candidates can answer it

### Estimate difference in defective units from production lines

Samples were taken of 400 units of each of the two production lines, X and W, of a manufacturing plant. The sample of the production line X had 40 defective units while the sample of line W had 80 defective units. Estimate the difference in the fraction of defective units produced by the two lines with a confidence coefficien

### Determine what is the minimum size of sample to be taken

You want to determine the size of sample needed to estimate the mean of a population with an error no greater than 1.6, with a probability of 95%. Based on previous experience you know that the standard deviation of the population is 12.7 Determine what is the minimum size of sample to be taken.

### Probability & Statistics

Wages of workers in a company have an average of \$38,000 and a standard deviation of \$2,500. They took in the company a sample of 60 workers' wages. a) Within which limits you would expect to find that the sample mean falls to a 95? b) Determine the probability of observing a sample mean more than \$38,600. c) What would

### Statistics Probability 3 problems

1. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in les

### Probability Distribution 3 problems

1. The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon. The probability of at least 3 accidents is ________. a. 0.25 b. 0.15 c. 0.75 d. 0.20 2. A certain type of new business succeeds 60% of the time. Suppos

### A General Rule Regarding the Amount of Capacity to Build

4. Chapter 12: Suppose we are considering the question of how much capacity to build in the face of uncertain demand. Assume that the cost is \$20 per unit of lost sales due to insufficient capacity and \$2 per unit due to excess capacity. Also assume that there is a cost of \$7 for each unit of capacity built. The probability of

### Binomial & Normal Probabilities..

1. CNBA basketball player Steve Swoopes scores on 85% of his foul shots. If he gets eight foul shots during a game, what is the probability that he will score on exactly seven of them? 2. A manufacturing company uses a binomial distribution to predict the number of defective units among its products. What is a "success" in t

### Statistics: Probability that new vehicles may require warranty service in first year

15. Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday. a. What is the probability that none of these vehicles requires warranty service? b. What is the probability exactly one of these vehicles requires

### Statistics Probability, distribution function: Delta Airlines, PGA golfers driving distance

1.) Delta Airlines quotes a flight time of 2 hrs, 5 minutes for its flights from Cincinnati to Tampa. We belive that actual flight times are uniformly distriubted between 2 hours and 2 hours 20 minutes. A.) show a graph of probabililty density function for flight time B.) what is the prob. that the flight will be no more than

### Probability: American Intellectual Union

See attached file. What is the distribution of individuals by gender? What is the "tenure with company" distribution by gender? What percentage of the survey participants are in each department? What is the sample mean for extrinsic value by gender? What is the probability that an individual will be between 16-21 year

### Desired failure rate, reliability analysis, confidence levels

A "one-shot" device can be used only once; after use, the device (e.g. a nuclear weapon, space shuttle, automobile air bag) either is destroyed or must be rebuilt. The destructive nature of a one-shot device makes repeated testing either impractical or too costly. Hence, the reliability of such a device must be determined with m

### Statistics: Probability Based on Exponential Distribution

An infestation of a certain species of caterpillar called the spruce budworm can cause extensive damage to the timberlands of the northern United States. It is known that an outbreak of this type of infestation occurs, on the average, every 30 years. Assuming that this phenomenon obeys an exponential probability law, what is

### Study of population concentrations in urban counties by Nevada commissioners

Researchers at the University of Nevada at Reno asked a sample of county commissioners to give their perception of the single most important factor in identifying study of urban countries (Professional Geographer, Feb. 2000.) In all, five factors were mentioned by the commissioners; total population, agricultural change, presenc

### Normal Approximation to Binomial

1. You attempt a 50 item (n = 50) true-and-false exam. You did not study for the material and your attempt to answer any item is a guess, with a 50% chance that you will get any item correct. You need a score of 30 or better to pass the exam. A. If you are truly guessing your way through the exam, what is the probability

### Statistics 5.1, 5.6, 5.10, 5.16, 5.18: Mean, variance, deviation, Poisson, probability

5.2 Determine the mean, the variance, and the standard deviation of the following discrete distribution. x P( x) 0 .103 1 .118 2 .246 3 .229

### Binomial Probability: Number of Accident Claims

Accident claims are checked for completeness by branch offices of Fortune Insurance before they are sent to a regional office for payment. Historically 80% of the claimes are complete whenthey reach the regional office. You select a random sample of 20 claimes that have arrived at the regional office. Find the probability of

### Normal Probability: Height of 10 year old boys

Height of 10 year kid boys. We've established that heights of 10 year old boys vary according to a normal distribution with a mean= 138 centimeters and standard deviation =7 centimeters. a) What proportion of this population is less than 150 centimeters tall? b.) What proportion is less than 140 centimeters in height? c) Wh

### Z-score, Normal Probability & Percentiles

1. Consider the following scores comprising a population of size N = 14 X F 14 1 13 2 12 4 11 3 10 2 9 2 A. What is the mean for these N = 14

### Probabilities about House Sales: Number of Days to Sell

5. A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed. a. Assuming the company's claim is true, if one home is selected at random, what is the probability that it