Suppose that monthly income follows a normal distribution with mu=$4.400 and sigma=$1,600 A government agency wants to provide free health care for all individuals who fall below a specific monthly income level but does not want to award this benefit to more than 33% of the population What is the income catoff for this proposed benefit where no more than 33% of the population will qualify (in other words , will fall below this level of income ?
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!
From the provided information,
Mean (µ) = 4400
Standard deviation (σ) = 1600
X~N (4400, 1600)
Here X be a random variable which represents the monthly income.
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