CENTRAL LIMIT THEOREM FOR AVERAGES
If we take samples of size n from a random
variable X which has any known or unknown
distribution and average the samples, the
averages will form a normal distribution, if n is
large enough.
Notation:
Let X =the random variable for the original
distribution
 X = the mean of the original distribution
 X = the stand. dev. of the original distribution
We use
X
= the random variable of averages
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X ~ N X ,
 X 
n
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The length of a particular type of criminal trial
has an unknown distribution with a mean of 21
days and a standard deviation of 7 days. A
random sample of 9 trials is taken.
a. X =
b. X ~
c. X =
d. X ~
e. What is the probability that the average
length of 9 trials is less than 23 days?
f. 90% of the average lengths of 9 criminal
trials are at most how long?