When Sandy made landfall in October of 2012, it became the second most costly hurricane in the US. As of March 2014, the estimated cost was over $68 billion. Much of the damage was caused by flooding. The rainfall in areas affected by Sandy follow a Normal distribution. The average rainfall during the storm was 7.3 inches with a standard deviation of 2.44 inches (www.accuweather.com). Areas in Maryland and New Jersey saw more rain than the other affected regions. (a) What is the probability that a randomly selected region had less than 5 inches of rain? (b) What is the probability that a randomly selected region had between 10 and 12 inches of rain? (c) What is the probability that a randomly selected region had more than 20 inches of rain?
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!
When Sandy made landfall in October of 2012, it became the second most costly hurricane in the US. As of March 2014, the estimated cost was over $68 billion. Much of the damage was caused by flooding. The rainfall in areas affected by Sandy follow a
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(a) What is the probability that a randomly selected region had less than 5 inches of rain?
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(b) What is the probability that a randomly selected region had between 10 and 12 inches of rain?
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(c) What is the probability that a randomly selected region had more than 20 inches of rain?
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(d) Find the 50th percentile of rainfall amounts. (HINT: NO WORK REQUIRED)
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(e) Find the 75th percentile (Q3) of rainfall amounts.
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