If we model after-tax household income with a normal distribution, then the figures of a study imply the information in the following table. Assume that the distribution of incomes in each country is normal. Country Country A Country B Country C Country D Country E Mean Household Income $23,000 $33,000 $13,000 $37,000 $29,000 Standard Deviation $29,000 $18,000 $15,000 $31,000 $11,000 What percentage of households in Country E are either very wealthy (income at least $75,000) or very poor (income at most $12,000)? (Round your answer to the nearest percent.) %
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!
| Country | Country A | Country B | Country C | Country D | Country E |
|---|---|---|---|---|---|
| Mean Household Income | $23,000 | $33,000 | $13,000 | $37,000 | $29,000 |
| Standard Deviation | $29,000 | $18,000 | $15,000 | $31,000 | $11,000 |
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