The average income tax refund for the 2017 tax year was $1997. Assume the refund per person follows the normal probability distribution with a standard deviation of $943. Use this model to answer the following questions. Don’t use Excel formulas – use the tables. Show the standardization and other calculations. a) For a randomly selected return, what the is probability that the refund exceeds $2500 ? b) For a randomly selected return, what the is probability that the refund is between $2000 and $3000? c) What is the 3rd quartile of the refund amount? d) The 20th percentile?
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!
The average income tax refund for the 2017 tax year was $1997. Assume the refund per person follows the
- a) For a randomly selected return, what the is probability that the refund exceeds $2500 ?
- b) For a randomly selected return, what the is probability that the refund is between $2000 and $3000?
- c) What is the 3rd
quartile of the refund amount?
- d) The 20th percentile?
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