1.  A farmer divided a field into 1-foot by 1-foot sections and tested soil samples from 32 randomly selected sections in the field. He finds that the mean pH level of the samples is 5.7 with a standard deviation of 0.26. (a)  Find the mean and standard deviation of the sampling distribution of all possible soil samples of size . Round to three decimal places. (b)  Construct a 95% confidence interval for the mean pH level of soil samples from every 1-foot by 1-foot section. Show your work. Even if you use technology, show the expression that is used to determine the margin of error for the interval. Interpret the interval in a complete sentence. (c)  The farmer tested soil samples from 34 randomly selected sections from another field. He found the mean pH level of those samples to be 6.1 with a standard deviation of 0.34. Construct a 95% confidence interval for the difference between the mean pH levels of all possible soil samples from both fields. Show your work. Even if you use technology, show the expression that is used to determine the margin of error for the interval. Interpret the interval in a complete sentence. Answer: ?

Instructions 1. Research some popular games of chance that Blaise Pascal or Daniel Bernoulli would have studied. Be prepared to explain the expected outcomes of these games and how this relates to the study of Probability. Find at least 2-3 different sources of information. 2. Create a new Microsoft Word (.doc / .docx) or Rich Text Format (.rtf) document on your computer, and write explaining the people identified above, their games of chance, the outcomes of these games, and how it relates to the study of Probability in your own words.