Summary statistics:

for sample of 20= variable 3 ( Age)

Column Mean Std. dev.

Age 31.1 5.5620897

For this problem only, assume that the sample mean and standard deviation for Variable 3 for the 20 sample values in your survey is the same as the population mean and standard deviation for Variable 3. Suppose that you were to randomly select a new sample of 40 customers from your survey population and observe their responses to Variable 3. Based on this new sample size, compute the following probabilities in Problems 5a and 5b below using your calculator and the appropriate statistical table. Also, for each problem below sketch the appropriate distribution with the probability in question appropriately shown. Note that based on the theory in this course you should be able to answer the problems below, without having to actually create a sample of 40 values for Variable 3.

Problem 5a Find the probability that the sample mean of Variable 3 (based on the 40 customer selected) is less than 90% of the population mean. [4 marks]

Problem 5b Find the probability that the sample mean (based on the 40 customer selected) will be within 5% of the population mean, on either side of the population mean. [4 marks]

Age (Variable 3)

25

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31

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20

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28

32