1. STA 2023 Section 5.4 Sampling Distributions and the Central Limit Theorem

2. Sampling Distributions 

3.  SampleMeanSampleMeanSampleMeanSampleMean 130,130130200,130165230,130180270,130200 130,200165200,200200230,200215270,200235 130,230180200,230215230,230230270,230250 130,270200200,270235230,270250270,270270

4. The Central Limit Theorem 

5. 

6. Probability and the Central Limit Theorem 

7.  Example 3: The average sales price of a single-family house in the United States is $290,600. You randomly select 12 single-family houses. What is the probability that the mean sales price is more than $265,000? Assume that the sales prices are normally distributed with a standard deviation of $36,000.  Answer:.9931  Interpretation: 99.31% of samples of 12 single-family houses will have a mean sales price greater than $265,000.

8. Notice the wording!  From consumer reports, the price for LCD monitors are normally distributed with a mean of $190 and a standard deviation of $48.  What is the probability that a randomly selected LCD monitor costs less than $200?  Answer:.5825  You randomly select 10 LCD monitors. What is the probability that their mean cost is less than $200?  Answer:.7449  Notice: If there is mention of looking at a sample from the population, you must use The Central Limit Theorem.