Question

# 1) A sample of 123 randomly selected students found that the proportion of the students planning to travel

home for Thanksgiving is 0.76. What is the standard deviation of the sampling distribution? Round to 3 decimal digits.

2) Suppose a sample space has things a, b, and c. Twice, draw from the sample space and replace. The possible sequences formed are (aa, ab, ac, ba, bb, bc, ca, cb, cc)

Now suppose there are Y different things. There are Y ways the first draw can occur. For each of the Y ways the first draw can occur, there are Y ways the second draw can occur, resulting in Y times Y, or Y2 sequences. For each of the Y2 sequences formed from 2 draws, there are Y ways the 3rd draw can occur forming y3 sequences. Generalizing, there are yX sequences formed by drawing X times from Y different things with replacement.

Example: the number of state license plates that can be made with 3 letters followed by 3 numbers is 26x26x26x10x10x10 = 26 3 x 10 3 = 17,576,000. From this one style of plate, there are many sequences.

How many sequences of 4 things can be formed from 8 different things with replacement and order is important?

3) A manufacturing process has acceptance limits 100 +or-3. A recent sample produced the measurement in file DATA. Assuming normal distribution, what percentage of the population does not meet the acceptance limits.

100.896

100.722

101.110

100.319

99.266

101.104

99.769

99.228

98.805

99.568

99.339

99.585

101.680

99.903

99.604

100.550

98.260

100.078

98.515

98.010

101.011

98.809

98.522

100.177

101.138

100.055

99.566

100.500

100.159

100.835

100.075

99.347

101.199

99.749

99.327

98.384

101.632

101.176

99.874

99.879

98.219

101.103

100.066

100.399

102.906

100.808

98.304

99.527

98.534

99.898

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