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Stat 401 Lab Activity 3 Wednesday, October 19, 2005 Part I. The Normal distribution. Read about the normal distribution from ch05t.pdf of the lecture notes (from page 12 until Proposition 3.4 on page 21). 1. Plotting the Normal Probability Density Function. We will plot normal pdfs through Minitab. These set of commands can be used for plotting the pdf of other random variables as well. a) Generate data from -3.4 to 3.4 in steps of 0.01: Calc>Make Patterned Data>Simple Set of Numbers> Store Patterned Data in “C1”; From first value “-3.4”; To last value “3.4”; In step of “0.01”, OK. b) Find the value of the probability density function of N(0,1) for each entry in C1: Calc> Probability Distributions > Normal> check “Probability Density”; enter “0” and “1” for Mean and Standard Deviation; enter “C1” and “C2” for Input column and Optional storage, OK. c) Do a scatter plot (with Connect Line) of C1 as X and C2 as Y. Next we will superimpose the plot of the pdf of N(0,1/16) to that of the pdf of N(0,1). Note that N(0,1/16) is the pdf of the sample mean of a sample of size n=16 from a N(0,1) population. d) Repeat step b), but change “1” to “0.25” for Standard Deviation, and enter “C3” for Optional storage. e) Graph> ScatterPlot > With Connected Line> input “C2” and “C1” under Y and X in the first row, and input “C3” and “C1” under Y and X in the second row; Click Multiple Graphs, select “Overlaid on the same graph”, OK, OK. 2. Finding Normal Probabilities and Population Percentiles To find a percentile, such as the 95th of a normal distribution, first enter “0.95” in a column, e.g. column c4, and follow the commands Calc> Probability Distributions> Normal> Select “Inverse cumulative probability”; fill “0 and 1” for Mean and Standard Deviation; select “C4” and “C5” for Input column and Optional Storage, OK. Several percentiles can be found at once, by entering, e.g.0.25, 0.5, 0.75, 0.950 in C4 and using the above sequence of commands. To find the cumulative distribution use the above sequence of commands except for selecting “Cumulative probability” instead of “Inverse cumulative probability”.. Part II. The Correlation Coefficient Copy the data in data.txt in two columns of Minitab and calculate the correlation coefficient. Stat > Basic Stat > Correlation > enter variable names or columns > OK