Normal Distribution Note: other distributions

– hypergoemetric - sampling with replacement

– beta

– bimodal

– VanGenuchten

Normal Probability Density Function– pdf:

221

2

1

xexf

Checking for normality»

» IQR/s =~ 1.3

» Normal probability plot

» Chi-square distribution

%1003

%952

%68

sx

sx

sx

Sampling Distributions– CHKOUT.XLS

» 500 data points

» = 50.1 , = 49.1

» take a random sample of 5 compute sample mean repeat 100 times

» now have a distribution of 100 sample means

» If we have a large sample size, the distribution of sample means:

is approximately normal, regardless of original distribution

mean of sample means = mean of population

standard deviation of sample means = population standard deviation / n

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?