Engineering Statistics Quiz 2 Exam Questions and Answers.

Engineering Statistics Quiz 2 Exam Questions and Answers Permutation Equation - Correct Answers: n = objects total r = objects selected Here order is important Combinations Equation - Correct Answers: n = objects total r = objects selected Here order is not important Baye's Theorem - Correct Answers: P(B|A) = [P(B_r) P(A/B_r)]/[∑ P(B_i) P(A/B_i)] B_i or B_r = is the % probability P(A/B_r) = is the fraction of the event (which is given) Conditional Probability - Correct Answers: Usually used when finding the probability of an event (A) happening given that another event (B) has occurred. Binomial Distribution - Correct Answers: b(x; n, p) = (n x) p^x (1-p)^(n-x) x = # of successes n = # of Bernoulli trials p = probability of success Note: If given B(x; n, p) then refer to the given table. Used when finding the probability of observing "x" successes in a "n"# of trials. (Successes is the number you count up to) Just a series of Bernoulli trials, used when their outcomes have no impact on future outcomes. The probability for success or failure is the same for each trial. For each trial: success = p failure = 1-p Hypergeometric Distribution - Correct Answers: h(x; n, a, N) = [(a x)(N-a n-x)]/(N n) x = probability of getting "x" successes (# we count up to) n = sample size a = # of successes in a lot N = lot/population size Used when you start sampling without replacement, this therefor changes the probability so trials are not independent. To check that your #'s are set up correctly: a+ (n-a) = N x+ (n-x) = n When the problem says: 'x' or more at least 'x' Take: 1 - sum of the probabilities Ex: for 2 more more: 1 - [P(x=0)+P(x=1)] When the problem says: anywhere from 'x' to 'x' Add all the probabilities. from 'x' to 'x' Poisson Process & Poisson Distribution - Correct Answers: A process controlled by some sort of chance mechanism, occurrences don't come in regular intervals. ƒ(x; λ) = [(λ^x)(e^-λ)]/x! x = # of occurrences λ = mean or average (µ) λ= np Usually used to determine the # of random occurrences of an event per unit of time, distance, volume, etc. It gives us the distribution of these random events. Poisson approximates the binomial distribution if 'n' is large and 'p' is small. When the problem says: 'x' or more at least 'x' Take: 1 - (sum of the probabilities) Ex: for 2 more more: 1 - [P(x=0)+P(x=1)] Geometric Distribution - Correct Answers: g(x; p) = p(1-p)^(x-1) x = # of trials needed to get to the 1st success p = probability of a success Usually used to determine the probability of getting the 1st success after a # of failures When the problem says on or before the 'x' trial: Sum all the probabilities starting at 1 Ex: occurs on or before the 3rd trial: P(x=1) + P(x=2) + P(x=3) Multinomial Distribution - Correct Answers: ∫(x₁,x₂,x₃) = [ n!/(x₁!x₂!x₃! ] (p₁^x₁) (p₂^x₂) (p₃^x₃) x = # of successes for each item p = probabilities for each item n = # of trials Its an extension of the binomial distribution. Has more than 2 exclusive outcomes Normal approximation to the binomial distribution - Correct Answers: z = X - np/[√(np(1-p)] np = mean np(1-p) = standard deviation n = # of units/trials p = probability Here the normal distribution can approximate the binomial distribution. Works better if 'p' is close to 0.5 and when 'n' is large. Needs a continuity correction. Exponential Distribution - Correct Answers: (1/B) e^(-x/B) It is a gamma distribution where α = 1 and its related to the random poisson process. This distribution is the time between observations for a poisson process. Normal Distribution - Correct Answers: Most important distribution otherwise known by its bell curve or the Gaussian distribution. Symmetrical about the mean. Area under the curve gives me a probability 68% of observations are found +- 1 std from mean 95% of observations are found +- 2 std from mean 99.7% of observations are found +-3 std from mean f(x; M, σ²) = [1/sqrt(2πy) ] e^((-x-µ)²/2/σ²) Lognormal Distribution - Correct Answers: 1/(√(2π)(β)) (x^-1) (e^(-(ln(x) - α)²/2β²) Occurs when we encounter a random variable which is such that its logarithm has a normal distribution. Parameters: α and β which are not the same as the uniform distributions, their values determine the shape of the distribution. Gamma Distribution - Correct Answers: (1/(β^α)r(α)) ( x^(α-1)) (e^(-x/β)) Used in reliability calculations. Parameters: α and β. If α = 1 the game distribution degenerates to the exponential distribution. Beta Distribution - Correct Answers: r(α+β) / [(r(α))(r(β))] (x^(α-1)) (1-x)^(β-1) When a random variable takes on values on the interval from 0 to 1 Parameters: α and β Frequently used for engineering project management: probability that a task will be completed on time, Parkinson's law, Student syndrome. Weibull Distribution - Correct Answers: α βx^(β-1) e^(-αx^β) Found when a random variable is normal distributed, but mean - some # of standard deviations cannot be less then 0. Parameters: α and β Central Limit Theorem - Correct Answers: Regardless of the underlying population, the mean of a sample becomes normally distributed as n→∞ . The CLT begins at 25→30 (n). Standardized sample mean is standard normally distributed. Equation is the "sample of values" X-Bar = mean of a random sample size µ = population mean σ = variance n = random sample size "T" Distribution - Correct Answers: (Distribution of the man) Similar shape to the standard normal distribution (symmetric around 0). Its shape varies according to its degrees of freedom. The "t" distribution converges to the standard normal as n→∞ X-Bar = mean of random sample size µ = mean from a normal population n = random sample size s or σ = variance Chi Squared Distribution - Correct Answers: Distribution of sample variance cannot be less than 0. Its shape depends on degrees of freedom. X²= random variable with the chi square distribution n = random sample size s² or σ = variance of random sample size The probability is the area to the right of the observed test statistics (what you get for x²) "F" Distribution - Correct Answers: F = s₁²/s₂² Represents the ratio of the sample variances of 2 normally distributed populations having the same variance. Parameters: numerator degrees of freedom = n₁-1 denominator degrees of freedom = n₂-1 The "F" table can yield values on both the left and right side of the distribution. Same graph as Chi squared Uniform Distribution - Correct Answers: All values of "x" from α→β (parameters) are equally likely Graph is a flat line Parkinson's Law - Correct Answers: Parkinson's law is the adage that "work expands so as to fill the time available for its completion". Student Syndrome - Correct Answers: Student syndrome refers to planned procrastination, when, for example, a student will only start to apply themselves to an assignment at the last possible moment before its deadline. This eliminates any potential safety margins and puts the person under stress and pressure. Walter Andrew Shewhart - Correct Answers: Was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control and also related to the Shewhart cycle. japan's manufacturing rise 1950's - Correct Answers: The economic history of Japan is most studied for the spectacular social and economic growth .... Increasingly, han authorities oversaw the rising agricultural production and the spread of rural handicrafts Quality is free - Correct Answers: by Phil" Crosby was a businessman and author who contributed to management theory and quality management practices Juran - Correct Answers: Joseph Moses Juran was a Romanian-born American engineer and management consultant. He was an evangelist for quality and quality management, having written several books on those subjects. William Edward Deming - Correct Answers: Deming offered 14 key principles to managers for transforming business effectiveness. Malcolm Baldrige National Quality Award - Correct Answers: The Malcolm Baldrige National Quality Award recognizes U.S. organizations in the business, health care, education, and nonprofit sectors for performance excellence Tom Peters - Correct Answers: Thomas J. Peters is an American writer on business management practices, best known for In Search of Excellence. Harley-Davidson - Correct Answers: Harley-Davidson, Inc., or Harley, is an American motorcycle manufacturer, founded in Milwaukee, Wisconsin in 1903. Ishikawa Diagrams - Correct Answers: Ishikawa diagrams are causal diagrams created by Kaoru Ishikawa that show the causes of a specific event. Common uses of the Ishikawa diagram are product design and quality defect prevention to identify potential factors causing an overall effect. Pareto Diagrams - Correct Answers: A Pareto chart, named after Vilfredo Pareto, is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line. SPC Charts - Correct Answers: The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit. These lines are determined from historical data. JIT - Correct Answers: is a methodology aimed primarily at reducing times within production system as well as response times from suppliers and to customers. Benchmarking - Correct Answers: Benchmarking is comparing ones business processes and performance metrics to industry bests and best practices from other companies 6 sigma - Correct Answers: Six Sigma is a disciplined, data-driven approach and methodology for eliminating defects (driving toward six standard deviations between the mean and the nearest specification limit) in any process - from manufacturing to transactional and from product to service. Motorola - Correct Answers: was an American multinational telecommunications company