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Find the sampling distribution of means if the Population is (5, 10, 15) and n = 3

Find the sampling distribution of means if the Population is (5, 10, 15) and n = 3. Sampling Distribution of a sample Means. Section 7.3. What should a sampling distribution for rolling 1 dice 20 times look like?.

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Find the sampling distribution of means if the Population is (5, 10, 15) and n = 3

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  1. Find the sampling distribution of means if the Population is (5, 10, 15) and n = 3

  2. Sampling Distribution of a sample Means Section 7.3

  3. What should a sampling distribution for rolling 1 dice 20 times look like?

  4. What should a sampling distribution for the mean when rolling 2 dice 20 times look like?

  5. What should a sampling distribution for the mean when rolling 10 dice 20 times look like?

  6. Simulation of Central Limit Theorem • http://onlinestatbook.com/simulations/CLT/clt.html • http://www.chem.uoa.gr/applets/appletcentrallimit/appl_centrallimit2.html *Averages are less variable than individual observations!

  7. 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)

  8. 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.

  9. Properties of a Sampling Distribution of Sample Means • Shape is approximately normal since • Population is normal, or • Central Limit Theorem (n  30)

  10. 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.

  11. Thus…..

  12. 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.

  13. 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?

  14. 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?

  15. Homework • Worksheet on SD of Means

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