Part 1 of 4 A beverage company has two bottling plants in different parts of the world. To insure uniformity in their product, the variances of the weights of the bottles at the two plants should be equal. But Stephanie, the company's vice president of quality assurance, suspects that the variance at bottling plant A is more than the variance at bottling plant B. To test her suspicions, Stephanie samples 37 bottles from bottling plant A and 33 bottles from bottling plant B, with the following results (in ounces): Bottling Plant A: 12.4, 12.4, 13.4, 14.3, 12.7, 12.7, 13.7, 12.4, 12.8, 12.4, 12.9, 12.7, 12.8, 13.3, 13.8, 12.7, 12.4, 11.9, 12.9, 13, 13.1, 12.4, 12.7, 12.6, 12.5, 13.3, 12.2, 13.3, 12.8, 12.7, 13.2, 13.1, 11.7, 13, 12.3, 13.1, 12.4
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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