Chapter5andQualityControl

# Chapter5andQualityControl - Section 5.2: Using the Normal...

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1 Section 5.2: Using the Normal Distribution with Sample Means, Quality Control Learning goals for this chapter: Define sampling variability and understand how to minimize it. Understand the difference between parameters and statistics. Explain how sampling distributions work. Define the Central Limit Theorem and know how to apply it. Distinguish between X and x problems. Distinguish between forwards and backwards x problems. State examples of processes and control vs. capability. Read, create, and interpret process control charts. Calculate upper and lower control limits and the center line for control charts. Know when a process is out of control. In section 1.3, we learned how to use the normal distribution for X if we knew the and and if X was Normally distributed. Here we will see how to use the normal distribution for sample means. You just have to use the right and , and everything else works just like in section 1.3. Normal distribution for X (Review of 1.3) What is X? X is a single score, account, height, or weight or scores (etc.) in general When do we use Normal distribution? if X is Normally distributed Mean and standard deviation of X: and (told to us in the problem) Formula we use for Z: X Z Normal distribution for X (Section 5.2) What is X ? X is the sample mean When do we use the Normal distribution? If X is Normally distributed, then X is too. However, according to the Central Limit Theorem , no matter what distribution the population has, as long as you draw a SRS (simple random sample) with a fairly large sample size (n), then the sample mean is Normally distributed. (This is a very nice and very big deal.)

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2 Mean and standard deviation of a sample mean: x x n Formula we use for Z : x x X Z How do you tell these “ X problems apart from section 1.3 “X” problems? Section 1.3
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## This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue.

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Chapter5andQualityControl - Section 5.2: Using the Normal...

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