MTH 147 – Fall 2015 Name:____

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MWF 8:05am – 8:55am CSU ID:___________________

Quiz 4

Instructions: Quiz is open book and open note. Read all questions carefully and present all answers within the provided space. If the space is not enough you may write on the back. All work must be shown to receive full credit, if applicable.

Total Points: 10
Question 1:
For the population of farm workers in New Zealand, suppose that weekly income has a distribution that is skewed to the right with a mean of µ = $500 (N.Z.) and a standard deviation of s = $160. A researcher, unaware of these values, plans to randomly sample 100 farm workers and use the sample mean annual income x ¯ to estimate µ.
Show that the standard deviation of x ¯ equals 16.0

Explain why it is almost certain that the sample mean will fall within $48 of $500.