A tire manufacturer hopes that their newly designed tires will allow a car traveling at sixty mph to come to a complete stop within an average of 125 feet after the brakes are applied. They will adopt the new tires unless there is strong evidence that the tires do not meet this objective (if the distance statistically greater than the expected, then it means the tires do not meet the objective). The distances for 9 sample stops on a test track were: 129, 128, 130, 132, 135, 123, 125, 128, and 130. What is the lower bound of 95% confidence interval for the population mean. 127.979 126.568 126.159 128.1115 none of above
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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