Ch6. "A carpet manufacturing company is comparing the tensile strengths of two different types of synthetic fiber. Synthetic fiber A used in manufacturing carpet has tensile strength that is normally distributed with mean 75 psi and standard deviation 12 psi, and synthetic fiber B has tensile strength that is 70 psi and standard deviation 12 psi. Random sample of nA = 16 and n8 = 9 of fiber specimens are selected. Find the probability that the sample mean of fiber specimen A exceeds the sample mean of fiber specimen B by 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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