# Lab 15 Worksheet

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Lab 10 Distribution of Sample Means
Worksheet Solutions

1. In your worksheet, record the mean of the first sample. How does this mean compare to
the mean of the population? How much sampling error is there (sampling error is the
difference between the population mean and the sample mean)?

2. What is the mean of the distribution of sample means? How does this mean of the
distribution of sample means compare to the actual population mean?

3. What are the means of each of these sampling distributions? How do they
compare? What are the standard errors (standard deviations of the sampling distributions)
for each other?

4. How do the shapes of these distributions look? Are they skewed or fairly
symmetrical? Which appears to be closer to Normal (hint: you can click the "fit normal"
boxes to overlay a normal distribution)?

5. The population parameters for the SAT are:  = 500,  = 100, and it is Normally
distributed. Your class with 50 students has the mean exam score of 530. What is the
probability of having a sample mean of 600 and higher?

6. Try another example with a different distribution: A bottling company uses a filling
machine to fill plastic bottles with cola. The bottles are supposed to contain 300
milliliters (ml). In fact the contents vary according to a normal distribution with a  = 298
ml and a standard deviation  = 3 ml. What is the probability that the mean contents of
the bottles in a six-pack is less than 295 ml?

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