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Describe, in your own words, the following terms and give an example of each. Probability Binomial experiment Population parameter Probability distribution Standard score Central limit theorem Standard error of the mean Normal distribution Standard normal distribution Continuity correction factor Term Probability Definition Example Probability is the chance that a If we rolled a standard 6-faced fair die particular outcome will occur when a once, the probability of getting a 6 is random experiment (such as tossing a 1/6; that is, if the die is rolled fair coin) is performed. Probability of repeatedly n number of times, in the an event A is the ratio of the number long run, we can expect 6 to occur of favorable outcomes to the total approximately (n/6) times. number of outcomes. Binomial Experiment An experiment that has the Tossing a fair coin. Here, the characteristic that the probability of probability of success (say, Head) in success remains the same no matter any toss is the same, that is ½. how many times the experiment is repeated. A parameter is a value (usually Population Parameter Average monthly salary of professors unknown and which therefore has to be estimated), used to represent a certain statistic. Probability Distribution Probability distribution of a variable Binomial distribution (Discrete), (discrete or continuous) is a list of Normal distribution (Continuous) probabilities associated with each of its possible values. It is also called probability mass function or simply probability function. Standard Score The standard score is the distance If a population has a mean of 15 and a that an observation (or statistic) is standard deviation of 2.5. Then the from the mean of its distribution in observation 17.5 would have a terms of its standard deviation units. standard score = (17.5 - 15)/2.5 = 1. Central Limit Theorem The central limit theorem says that If samples of size n are drawn from a the sample means follow an population, the sample mean(x-bar) increasingly normal distribution as the will be close to the population mean sample size increases. In particular, () whereas the sample standard the mean of the sampling distribution deviation, s = Population standard is the same as that of the population deviation,/n and the standard deviation is the population standard deviation divided by the square root of the sample size. Hence, the larger the sample, the smaller the standard deviation of the sampling distribution. Standard Error of the Mean The standard error of the mean is the For a sample of size 16 with a standard deviation of the sampling population standard deviation of 5, distribution. In particular, it is the the standard error of the mean is population standard deviation divided 5/16 = 1.25 by the square root of the sample size, that is s = /n. Normal Distribution The normal distribution is a The diameters of bolts produced by a continuous, real valued, symmetric, machine may be normally distributed bell-shaped distribution with two with a mean of 0.75 inches and a parameters, the mean () and the standard deviation of 0.25 inch. standard deviation (). It is a particular type of normal A normal distribution with = 0 and distribution with mean of = 0 and = 1. standard deviation of = 1. Problems on normal distribution are usually solved by using this distribution. Because there are an infinite number Standard Normal Distribution of possible normal distributions, one table (the standard normal table) is used to calculate all normal probabilities. Finding standard scores (z- scores) transforms any normal distribution into a standard normal distribution. Continuity Correction Factor A correction factor that is used when To find the probability of getting 623 binomial probabilities are calculated heads when a fair coin is tossed 1000 using the normal distribution times, assumption. n = 1000, p = ½, q = ½ m = np = 500, s = (npq) = 15.81 z = (x - m)/s z1 = (622.5 - 500)/15.81 = 7.75 and z2 = (623.5 - 500)/15.81 = 7.81 P(623 Heads) = P(7.75 < z < 7.81), which is almost 0.