http://www.ck12.org Chapter 7. Sampling Distributions and Estimations
The calculator has given an answer that is more accurate than that given in the chart. However, if the answer is
rounded to the nearest ten-thousandth, then both answers would be the same. Using the calculator is a more efficient
method of obtaining thez−score since you all have them on hand.
Example:For a normal distribution curve based on values ofσ=5 andμ=20, find the area betweenx=24 and
x=32.
Solution:
z=
x−μ
σand z=
x−μ
σ
z=24 − 20
5
and z=32 − 20
5
z= 0. 8 and z= 2. 4Using the TI-83
The area forz= 0 .8 is 0.2881 and forz= 2 .4 is 0.4918. Therefore the area betweenx=24 andx=32 is:
0. 4918 − 0. 2881 = 0. 2037
This means that the relative frequency of the values betweenx=24 andx=32 is 20.37%.
Central Limit Theorem
The Central Limit Theorem is a very important theorem in statistics. It basically confirms what might be an intuitive
truth to you: that as you increase the number of trials of a random variable, the distribution of the sample trials better
approximates a normal distribution.
Before going any further, you should become familiar with (or reacquaint yourself with) the symbols that are
commonly used when dealing with properties of the sampling distribution of the sample mean. These symbols
are shown in the table below:
TABLE7.2:
Population Parameter Sample Statistic Sampling Distribution
Mean μ x ̄ μx ̄
Standard Deviation σ s Sx ̄orσx ̄
Size N nIn the previous lesson, you discovered that the standard error is the standard deviation of the sampling distribution
and this value was calculated by using the formulas=
√
P·Q
n. By making a few substitutions, this formula can be