# Ch11 - Chapter 11 Inferential Statistics These Notes are...

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Chapter 11 – Inferential Statistics These Notes are taken from A Mathematical View of our World , Parks, Musser, et. al., 1 st custom ed., Thomson Publishing and the accompanying Instructor’s Resource CD. All rights reserved by the publisher. Sec 11.1 and 11.2 – Normal Distribution and Applications Goals o Study normal distributions o Study standard normal distributions o Find the area under a standard normal curve o Study normal distribution applications o Use the 68-95-99.7 Rule o Use the population z -score The process of making predictions about an entire population based on information from a sample is called ___________________________ . One way that’s done is to recognize that the data fits a normal distribution and then use those properties to make predictions. Normal Distributions (bell-shaped curves) are: 1) Symmetric about the mean 2) Have a well-defined peak in the middle of the distribution (mean = median = mode) 3) Most of the values are clustered near the mean, evenly on both sides (see 68-95-99.7 rule in a moment) 4) Larger deviations from the mean are increasingly rare (i.e. the further the value is from the mean, the less frequent that value is for the distribution) The mean and standard deviation determine the exact shape and position of the curve. Study Example 11.2 (pg 704) Example: (use picture for #12 on p. 712) Which data set has the largest mean? ____ ,the smallest mean? ____, the largest standard deviation? ____, the smallest standard deviation? ____ We will use the following fact to help us solve problems with this type of distributions: The percent of the total area under the curve between any two values = percent of data between those two values. 1

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Example: (we will draw a picture here in class) Suppose the figure represents the distribution of heart rates for men in the USA. 1) What percent of men have heart rates between 65 and 70? 2) What percent of men have heart rates between 75 and 78? 3) What percent of men have heart rates between 62 and 75? 4) What percent of men have heart rates above 78? 5) What percent of men have heart rates below 78? 6) Suppose you have a random sample of 100 men. How many men in the sample would you expect to have heart rates over 78? The 68-95-99.7 Rule NOTE: See p. 705, figure 11.7 to see part of the following demonstrated with 3 different “shaped” normal curves. For all normal distributions : o Approximately 68% of the measurements lie within 1 standard deviation of the mean. o
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Ch11 - Chapter 11 Inferential Statistics These Notes are...

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