17. In Problem 11 from the previous section, westated that the damage amount is normally distributed. Suppose instead that the damage amount istriangularly distributed with parameters 500, 1500,and 7000. That is, the damage in an accident canbe as low as $500 or as high as $7000, the mostlikely value is $1500, and there is definite skewnessto the right. (It turns out, as you can verify in @RISK,that the mean of this distribution is $3000, thesame as in Problem 11.) Use @RISK to simulatethe amount you pay for damage. Run 5000 iterations. Then answer the following questions. Ineach case, explain how the indicated event wouldoccur.a. What is the probability that you pay a positiveamount but less than $750?b. What is the probability that you pay more than$600?c. What is the probability that you pay exactly $1000(the deductible)?
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!
17. In Problem 11 from the previous section, we
stated that the damage amount is
triangularly distributed with parameters 500, 1500,
and 7000. That is, the damage in an accident can
be as low as $500 or as high as $7000, the most
likely value is $1500, and there is definite skewness
to the right. (It turns out, as you can verify in @RISK,
that the mean of this distribution is $3000, the
same as in Problem 11.) Use @RISK to simulate
the amount you pay for damage. Run 5000 iterations. Then answer the following questions. In
each case, explain how the indicated event would
occur.
a. What is the probability that you pay a positive
amount but less than $750?
b. What is the probability that you pay more than
$600?
c. What is the probability that you pay exactly $1000
(the deductible)?
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