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12-100hw3 - 12-100 Introduction to Civil and Environmental...

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12-100 Introduction to Civil and Environmental Engineering Spring 2008 Homework 3. Due: 6 February 2008 Assume that every quantity is valid to three significant figures. 1. You have a summer job doing engineering quality control at a microbrewery. The “brewmaster” makes only one type of ale, but that person is quite inexperienced and the ale varies from batch to batch. You measure the alcohol content (percentage) for ten batches and obtain: 5.7, 6.1, 6.1, 4.9, 5.8, 5.5, 6.3, 5.1, 5.4, and 6.0 percent. Determine the sample mean and the sample standard deviation of these data. Making the assumption that the alcohol content of any batch is a normally distributed random variable, determine the probability that the next batch will have an alcohol content less than 4.4 percent. Similarly, determine the probability that the next batch will have an alcohol content greater than 6.0 percent. Finally, determine the probability that the next batch will have an alcohol content somewhere between 4.5 and 5.5 percent.
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