o o N population size o n Total sample sizeo Xi Number of items in the

# O o n population size o n total sample sizeo xi

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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 Distributions 10/25/2015 ° 6.1 The Normal Probability Distribution Is a bell-shaped distribution with the following properties: o 1. It is unimodal; that is, the normal distribution peaks at a single value o 2. 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 identical o 3. The mean, median, and mode are equal o 4. 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. o 5. The amount of variation in the random variable determines the height and spread of the normal distribution ° Normal Probability Density Function x – any value of the continuous random variable o – population standard deviation Pie – 3.14159 e – Base of the natural log = 2.71828… u – population mean ° Finding Normal Probabilities Because x is a continuous random variable, the probability, P(x), is equal to 0 for any particular x The 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 distribution A normal distribution that has a mean = 0.0 and a standard deviation = 1.0 The horizontal axis is scaled in z-values that measure the number of standard deviations a point is from the mean Values above the mean have positive z-values Values below the mean have negative z-values z – scaled value (the number of standard deviations a point x is from the mean) x – any point on the horizontal axis u – mean of the specific normal distribution o – standard deviation of the specific normal distribution Any 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 example If x is distributed normally with mean of 100 and standard deviation of 50, the z-value for x = 250 is Z = 250-100 / 50 = 3.0 This means that x = 250 is three standard deviations (3 increments of 50 units) above the mean of 100. ° The standard normal distribution table Provides probabilities (or areas under the normal curve) associated with different z-values Is 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 Distributions 10/25/2015 ° 7.1 Sampling Error: What is it and Why it happens  • • • 