Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 5 Probability Distributions 193

Figure 5-8 compares the distribution of the random sample after

50 shots and after 500 shots. Note that the larger sample size more

closely follows the underlying probability distribution.

Figure 5-8

Distribution

after 50

and 500

observations

sample size = 50 sample size = 500

3 Try generating some more random samples of various sample sizes.

When you are fi nished, close the Random Samples workbook.

The Normal Distribution

In the Exploring Random Samples workbook, you worked with a distribu-

tion in the form of a bell-shaped curve, called the normal distribution. This

common probability distribution is probably the most important distribu-

tion in statistics. There are many real-world examples of normally distrib-

uted data, and normally distributed data are assumed in many statistical

tests (for reasons you’ll understand shortly). The probability density func-

tion for the normal distribution is

Normal Probability Density Function

f^1 y^25

1

s" 2 p

e^21 y2m^2

(^2) / 2 s 2
s.0, 2,m,, 2,y,
The normal distribution has two parameters, m (pronounced “mu”) and s
(pronounced “sigma”). The m parameter indicates the center, or mean, of the
distribution. The s parameter measures the standard deviation, or spread, of the
distribution. To see how these parameters affect the distribution’s location and
shape, you can work with the instructional workbook named Distributions.