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Find the sampling distribution of means if the Population is (5, 10, 15) and n = 3
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Sampling Distribution of a sample Means
Section 7.3
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What should a sampling distribution for rolling 1 dice 20 times look like?
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What should a sampling distribution for the mean when rolling 2 dice 20 times look like?
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What should a sampling distribution for the mean when rolling 10 dice 20 times look like?
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Simulation of Central Limit Theorem
*Averages are less variable than individual observations!
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Central Limit Theorem When n is sufficiently large, the sampling distribution of is well approximated by a normal curve, even if the population distribution is not itself normal. (if n>30)
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To clarify: A sample mean ( ) based on a large n will tend to be closer to the population mean ( ) than one based on a small n. The larger the sample size, n, the smaller the standard deviation.
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Properties of a Sampling Distribution of Sample Means
Shape is approximately normal since Population is normal, or Central Limit Theorem (n 30)
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If a population has a mean equal to 52 and a standard deviation equal to 3.4 and n = 100
What is the mean of the sample mean? What is the standard deviation of the sample mean? Describe the shape of the sampling distribution.
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Thus…..
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The amount of spaghetti sauce that fills a glass jar is normally distributed with and Find the probability that A jar, selected at random, is between 848 g. and 855 g. A sample of 24 jars has a mean weight between 848 and 855 grams.
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The heights of kindergarteners are approximately normal with and
The heights of kindergarteners are approximately normal with and A class of 30 is used as a sample. What is the probability that the sample mean is between 38 and 40? What would be different if I only asked the probability of finding a randomly selected kindergartner who is between 38 and 40 inches?
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The mean of song duration is and
The mean of song duration is and If the population is normally distributed, find the probability that in a sample of 30 songs, the duration is more than 14.5 seconds?
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Homework Worksheet on SD of Means
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