A water company wants to analyze the the level of a particular contaminant in a water supply. The contaminant level is to be checked at several locations. Assume that the observed contaminant level is normally distributed and that each observation is independent of the others. A scientist measures the contaminant level at 10 different locations in the water supply and finds the mean level of the substance is T = 120 parts per billion (ppb) with standard deviation s = 25 ppb. Estimate the true mean contaminant level in the water supply with a 99% upper confidence bound. Answer reguires 2 decimal places accuracy.
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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