Statistics 300: Elementary Statistics Section 6-5.

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Presentation transcript:

Statistics 300: Elementary Statistics Section 6-5

Central Limit Theorem Given: X has mean =  and standard deviation =  For a specified sample size “n” The number of possible samples of size n is usually very large

Central Limit Theorem The number of possible samples of size n is usually very large Example: Population N = 100 and sample size n = 10. The number of possible samples is 100 C 10 = 1.73 * 10 13

Central Limit Theorem Each of the possible samples has its own sample mean The collection (set or population) of possible sample means has a mean and standard deviation The mean =  and the standard deviation =  /sqrt(n)

Central Limit Theorem Furthermore, If n > 30 or if X~N(  ) then The distribution of all possible sample means is approximately a normal distribution

The Mean of a Random Sample has the distribution below if n > 30 or the “parent population” is “normal”

Weights of oranges have a mean weight of 34.2 grams and a standard deviation of 6.4 grams. If 12 oranges are selected at random, what is the probability the average weight of the 12 oranges will be greater than 30 g?