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Making high-stakes insurance decisions. The Journal of
Chapter 4, Problem 81E(choose chapter or problem)
Problem 81E
Making high-stakes insurance decisions. The Journal of Economic Psychology (Sep. 2008) published the results of a high-stakes experiment where subjects were asked how much they would pay for insuring a valuable painting. The painting was threatened by fire and theft, hence, the need for insurance. To make the risk realistic, the subjects were informed that if it rained on exactly 24 days in July, the painting was considered to be stolen; if it rained on exactly 23 days in August, the painting was considered to be destroyed by fire. Although the probability of these two events, “fire” and “theft,” was ambiguous for the subjects, the researchers estimated their probabilities of occurrence at .0001. Rain frequencies for the months of July and August were shown to follow a Poisson distribution with a mean of 10 days per month.
a. Find the probability that it will rain on exactly 24 days in July.
b. Find the probability that it will rain on exactly 23 days in August.
c. Are the probabilities, parts a and b, good approximations to the probabilities of “fire” and “theft”?
Questions & Answers
QUESTION:
Problem 81E
Making high-stakes insurance decisions. The Journal of Economic Psychology (Sep. 2008) published the results of a high-stakes experiment where subjects were asked how much they would pay for insuring a valuable painting. The painting was threatened by fire and theft, hence, the need for insurance. To make the risk realistic, the subjects were informed that if it rained on exactly 24 days in July, the painting was considered to be stolen; if it rained on exactly 23 days in August, the painting was considered to be destroyed by fire. Although the probability of these two events, “fire” and “theft,” was ambiguous for the subjects, the researchers estimated their probabilities of occurrence at .0001. Rain frequencies for the months of July and August were shown to follow a Poisson distribution with a mean of 10 days per month.
a. Find the probability that it will rain on exactly 24 days in July.
b. Find the probability that it will rain on exactly 23 days in August.
c. Are the probabilities, parts a and b, good approximations to the probabilities of “fire” and “theft”?
ANSWER:
Solution :
Step 1 of 3:
Given the number of days it will rain in the month of July is 24 days and
The number of days it will rain in the month of August is 23 days.
From the given information we know that the months of July and August it follows the poisson distribution with a mean of 10 days per month.
Our goal is :
a). We need to find the probability that it will rain on exactly 24 days in July.
b). We need to find the probability that it will rain on exactly 23 days in August.
c). We need to find to find are the probabilities, parts (a) and (b), good approximation to
the probabilities of “fire” and “theft”.
a). Now we have to find the probability that it will rain on exactly 24 days in July.
We assume that x is the the number of days it will rain in the month of July.
Here X follows a Poisson distribution with mean = 10.
The formula for the Poisson distribution is
P(x) = , x=0, 1, 2,...,
=10.
The the probability that it will rain on exactly 24 days in July is
P(x=24) =
P(x=24) =
P(x=24) = 0.00007317
Therefore, the probability that it will rain on exactly 24 days in July is 0.00007317.