Chapter 7
TheCentral Limit Theorem for Means, and theCentral Limit Theorem for Sums. Both
are concerned with drawing finite samples (with sizen) from a population with a known mean
(μ) and standard deviation (σ).
Central Limit Theorem of Means:
1. The normal distribution has thesame meanas the original distribution.
2. The normal distribution has a standard deviation that is equal to the original standard
deviation (σ) divided by the square root of the sample size (√𝑛).
NOTE: The variablenis the number of values that are averaged together, not the number
of times the experiment is done.
Central Limit Theorem for Sums:
The Central Limit Theorem for Sums states that the mean of the normal distribution of
sumsis equal to:
(n)(μX)=(150)(7.2)=1080
.
The Central Limit Theorem for Sumsstates the standard deviation of the normal
distribution of sums equal to:
(σX)(
√
n)=
(
1.2
)
(
√
150
)
≈14.70
Input the parameters into thenormalcdf()function asfollows: normalcdf(85,92,0,15/√31)as the
format for normalcdf function is normalcdf(lower value, upper value,μ,𝜎/√𝑛). After pressing
enter, thecalculator displays a value closer to0.7368.
Chapter 12
