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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