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Normal Distribution u Note: other distributions –hypergoemetric - sampling with replacement –beta –bimodal –VanGenuchten u Normal Probability Density Function.

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Presentation on theme: "Normal Distribution u Note: other distributions –hypergoemetric - sampling with replacement –beta –bimodal –VanGenuchten u Normal Probability Density Function."— Presentation transcript:

1 Normal Distribution u Note: other distributions –hypergoemetric - sampling with replacement –beta –bimodal –VanGenuchten u Normal Probability Density Function –pdf:

2 u Checking for normality »IQR/s =~ 1.3 »Normal probability plot »Chi-square distribution

3 u Sampling Distributions –CHKOUT.XLS »500 data points »  = 50.1,  = 49.1 »take a random sample of 5 u compute sample mean u repeat 100 times »now have a distribution of 100 sample means »If we have a large sample size, the distribution of sample means: u is approximately normal, regardless of original distribution u mean of sample means = mean of population u standard deviation of sample means = population standard deviation / n

4 u Example 6.16 –Before: LCN  = 60,  = 10 –take random sample of 40 concrete blocks –a. if no different after… –b. If after is no different, find the probability that the sample mean exceeds 64 –c. if sample mean = 73, is new better than old?

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