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ooN – population sizeon – Total sample sizeoXi – Number of items in the population with outcome ioxi – Number of items in the sample with outcome i°Hypergeometric Distribution ExampleExample: 3 light bulbs were selected from 10. Of the 10 there were 4 defective. What is the probability that 2 of the 3 selected are defective?
Chapter 6: Introduction to Continuous Probability Distributions10/25/2015°6.1 The Normal Probability DistributionIs a bell-shaped distribution with the following properties:o1. It is unimodal; that is, the normal distribution peaks at a single valueo2. It is symmetrical; this means that the two areas under the curve between the mean and any two points equidistant on either side of the mean are identicalo3. The mean, median, and mode are equalo4. The normal approaches the horizontal axis on either side of the mean toward plus and minus infinity. In more formal terms, the normal distribution is asymptotic to the x axis.o5. The amount of variation in the random variable determines the height and spread of the normal distribution°Normal Probability Density Functionx – any value of the continuous random variable o – population standard deviationPie – 3.14159e – Base of the natural log = 2.71828…u – population mean°Finding Normal ProbabilitiesBecause x is a continuous random variable, the probability, P(x), is equal to 0 for any particular xThe probability for an range of values between x1 and x2 is defined by the area under the curve between these two values.P(a < x < b)°The standard normal distributionA normal distribution that has a mean = 0.0 and a standard deviation = 1.0The horizontal axis is scaled in z-values that measure the number ofstandard deviations a point is from the meanValues above the mean have positive z-valuesValues below the mean have negative z-values
z – scaled value (the number of standard deviations a point x is fromthe mean)x – any point on the horizontal axisu – mean of the specific normal distributiono – standard deviation of the specific normal distributionAny normal distribution (with any mean and standard deviation combination) can be scaled into the standard normal distribution (z)Any specific value, x, from the population distribution can be converted into a corresponding z-value°The standard normal distribution exampleIf x is distributed normally with mean of 100 and standard deviation of 50, the z-value for x = 250 isZ = 250-100 / 50 = 3.0This means that x = 250 is three standard deviations (3 increments of 50 units) above the mean of 100.°The standard normal distribution tableProvides probabilities (or areas under the normal curve) associated with different z-valuesIs constructed so that the probabilities provided represent the chance of a value being between a positive z-value and its population mean, 0.
Chapter 7: Introduction to Sampling Distributions10/25/2015°7.1 Sampling Error: What is it and Why it happens