How to Solve Problems Involving Sampling Distributions
State: Express the problem in terms of the observed sample statistic.
Plan: Verify that all conditions have been met. Describe the shape, center, and
spread of the sampling distribution.
Do:
Perform calculations
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Standardize the sample statistic to restate the problem in terms of a standard
Normal variable z
Use Table A (or calculator) and the fact that the total area under the curve
is 1 to find the required area under the standard Normal curve
Conclude:
Write your conclusion in the context of the problem.
Example: Cereal Milk
A USA Today poll asked a random sample of 1012 U.S. adults what they do with the milk
in the bowl after they drink the cereal. Of the respondents 67% said that they drink it.
Suppose that 70% of U.S. adults actually drink the cereal milk.
Find the probability of obtaining a sample of 1012 adults in which 67% or fewer say they
drink the cereal milk. Do you have any doubts about the results of this poll?
Solving Problems involving Sampling Distributions
1. State: Express the problem in terms of the observed sample statistic.
2. Plan: Verify that all conditions have been met. Describe the shape,
center, and spread of the sampling distribution.
3. Do: Perform calculations. Standardize sample statistic in terms of z.
Use Table A.
4. Conclude: Write your conclusion in the context of the problem.