The minister of environment in a certain country decided to investigate whether expansion of a aluminum plant in that country would affect fluoride pollution in it's environment. The productions occurred the years 2005 and 2006. One of the things measured was the amount of fluoride in lamb jaws. The data available are measurements of fluoride in the jaws of 8 lambs that were slaughtered in the year 2004 and 8 lambs that were slaughtered in the year 2007. The data is shown below, along with a R output that can simplify your calculations. Fluoride amount 2004 (ug/g) | Fluoride amount 2007 (ug/g) 131.37 655.09 252.74 541.37 81.29 564.58 225.55 617.97 222.44 472.54 68.29 606.62 227.55 500.80 111.86 394.67 > fs2004<-c(131.37,252.74,81.29,225.55,222.44,68.29,227.55,111.86) > fs2007<-c(655.09,541.37,564.58,617.97,472.54,606.62,500.80,394.67) > mean (fs2004) [1] 165.1363 > mean(fs2007) [1] 544.205 > var (fs2004) [1] 5555.906 > var (fs2007) [1] 7348.022 > d<-fs2007-fs2004 > mean (d) [1] 379.0688 > var (d) [1] 14657.70
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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