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# STAT 110: Notes for Week of 9/27/16 STAT 110

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This 4 page Class Notes was uploaded by runnergal on Sunday October 2, 2016. The Class Notes belongs to STAT 110 at University of South Carolina taught by Dr. Wilma J. Sims in Fall 2016. Since its upload, it has received 4 views. For similar materials see Introduction to Statistical Reasoning in Statistics at University of South Carolina.

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Date Created: 10/02/16

STAT 110 – Notes for Week of 9/27/16 Chapter 13 Continued o Normal curve: a symmetric bell-shaped curve. A normal curve is described by its mean and standard deviation. The mean of a normal curve identifies the center of a distribution. The mean determines the location of the curve on a graph. The standard deviation determines the shape of a normal curve; as the standard deviation gets larger, the normal curve becomes more spread out and the peak of the curve is less sharp. o 68-95-99.7 Rule (Empirical Rule): in a normal distribution with a normal curve, about 65% of the data fall within one standard deviation of the mean, about 95% of the data fall within two standard deviations of the mean, and about 99.7% of the data fall within three standard deviations of the mean. When the curve is broken up into six standard deviations (three standard deviations on either side of the mean), 34% of the data fall in each first standard deviation of either side of the mean; 13.5% of the data fall in each area between the first standard deviation and the second standard deviation on either side of the mean, and 2.35% of the data fall in each area between the second deviation and the third deviation on either side of the mean. Essentially, this means that half of the data for one standard deviation away from the mean is on the left side of the mean and the other half of the data on the right side of the mean. 34% of the data on the left side of the mean + 34% of the data of the right side of the mean = 68% of the data, which is how much data is one standard deviation away from the mean. You can do these calculations for this rule for each standard deviation. o Standard score: the observations expressed in standard deviations above or below the mean. This is helpful when comparing similar data that use different variables. Standard score = (observation – mean)/standard deviation. observation = (standard score*standard deviation) + mean o cth percentile: a value where c% of the data lie below the value. For example, at the 60 percentile, 60% of the data lie below the 60 th percentile. All standard scores have corresponding percentiles. Table B (a table in the textbook that students will be given during the exam) gives all standard scores and their correlated percentiles. Chapter 17 o Chance behavior is unpredictable in the short run; however, chance behavior usually has a predictable pattern after many repetitions. This predictable behavior precludes the theory of probability. o Probability (P): a number between 0 and 1 that identifies the proportion of times a certain outcome occurs in the long run. This number cannot be less than zero, greater than one, or negative. o An impossible outcome has a probability of zero. o An assured outcome has a probability of one. o Random: when individual outcomes are uncertain but a predictable pattern emerges in the long run. o Sample space (s): group of all possible outcomes. o Event: group of some possible outcomes. o Experimental probability: proportion of the number of times a particular event occurs. This is an exact number that is determined through an experiment of many trials. o Theoretical probability: an estimate of the proportion of the number of times a particular event occurs when all outcomes are equally likely. P = (the number of ways an event can occur)/(the number of possible outcomes in a situation) o Short-run regularity myth: phenomena that have patterns in the long run do not need to have patterns in the short run. o Surprising coincidence/unusual event myth: sometimes coincidences are more likely than we think; we just need to look at the data differently. o Law of averages: averages become more stable as the number of trials increases, since each subsequent trial is part of a larger proportion and has a smaller effect on the average individually. In the short run, however, anything is possible. o Personal probability: what a person thinks the probability of an event is. This does not have to be based on data. It cannot be right or wrong, since it is someone’s opinion. It is a number between zero and one. Chapter 18 o Probability model: identifies all potential outcomes and assigns probabilities to those outcomes/collections of outcomes. o Mutually exclusive events: events that have no outcomes in common. o Probability rules i. All probabilities fall within the range of zero and one. ii. When all possible outcomes are added together, they should equal one. iii. Complement rule: the probability that an event doesn’t occur is equal to 1 – the probability that the event does occur. c A = complement of A. iv. If and only if two events are mutually exclusive, then the sum of their probabilities is equal to the probability that one or the other event occurs. P (A or B) = P(A) +P(B) If P is greater than one, then the events are not mutually exclusive.

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