Seven randomly selected plants that bottle the same beverage implemented a time management program inhopes of improving productivity. The average time, in minutes, that it took the companies to produce the samequantity of bottles before and after the program are listed below. Assume the two population distributions arenormal. Construct a 90% confidence interval for µd. Assume that the paired data came from a population that is normally distributed. Plant 1 2 3 4 5 6 7 Before 75 89 31 90 120 50 40 After 70 80 30 85 100 49 42
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!
Seven randomly selected plants that bottle the same beverage implemented a time management program in
hopes of improving productivity. The average time, in minutes, that it took the companies to produce the same
quantity of bottles before and after the program are listed below. Assume the two population distributions are
normal. Construct a 90% confidence interval for µd. Assume that the paired data came from a population that is
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