According to Internal Revenue Service, the average income tax refund for the 2011 tax year was $2,950. Assume the refund per person follows the normal probability distribution with a standard deviation of $950. a. What is the probability that a randomly selected tax return refund from the 2011 tax year will be 1. More than $2,000? 2. between $1,000 and $2,500? 3. between $3,200 and $4,000? b. What refund amount represents the 40th percentile of tax returns?
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!
1. More than $2,000?
2. between $1,000 and $2,500?
3. between $3,200 and $4,000?
b. What refund amount represents the 40th percentile of tax returns?
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