A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The force in kilograms (kg) applied to the tablet varies a bit and follows the Normal distribution with mean 11.5 kg and standard deviation 0.2 kg. The process specifications call for applying a force between 11.2 and 12.2 kg. i. What percent of tablets are subject to a force that meets the specifications? ii. The manufacturer adjusts the process so that the mean force is at uie center of the specifications, u = 11.7 kg. The standard deviation remains 0.2 kg. What percent now meets the specifications? iii. Calculate the 25th percentile (P2s) and the 75th percentile (P7s) of the distribution.
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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