According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847 (Time.com website). Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800. a. What is the probability that a household in Maryland has an annual income of $100,000 or more? b. What is the probability that a household in Maryland has an annual income of $40,000 or less? d. What is the probability that a household in Maryland has an annual income between $50,000 and $70,000? d. What is the annual income of a household in the 90th percentile of annual household income in Maryland?
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!
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847 (Time.com website). Assume that annual household income in Maryland follows a
a. What is the probability that a household in Maryland has an annual income of $100,000 or more?
b. What is the probability that a household in Maryland has an annual income of $40,000 or less?
d. What is the probability that a household in Maryland has an annual income between $50,000 and $70,000?
d. What is the annual income of a household in the 90th percentile of annual household income in Maryland?
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