Emissions of nitrogen oxides, which are major constituents of smog, can be modeled using a normal distribution. Let x denote the amount of this pollutant emitted by a randomly selected vehicle (in parts per billion). Suppose the distribution of x can be described by a normal distribution with μ = 1.5 and σ = 0.4. Suppose that the EPA wants to offer some sort of incentive to get the worst polluters off the road. What emission levels constitute the worst 10% of the vehicles? (Round your answer to three decimal places.) The worst 10% of vehicles are those with emission levels greater than ______ parts per billion. You may need to use the appropriate table in Appendix A to answer this question.
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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