Question 468149: Can someone please show me how to preform these two problems? I am completely lost.
9. A two year extended warranty on a computer costs $40. Suppose during these two years the
probability that the computer will need a minor repair is 0.05, and a major repair 0.01. Further
suppose a minor repair costs $200 and a major repair $500. What is the warranty issuer’s expected
profit from selling the policy?
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10. Suppose the expected life of a certain type of fruit fly is 100 hours with a standard deviation
of 15 hours. According to the Chebychev’s inequality, the
probability that a randomly selected fruit fly will live between 70 and 130 hours is at least _______.
Answer by ccs2011(207)   (Show Source):
You can put this solution on YOUR website! *******************************
9)Find the expected value of the warranty
The expected value is like a weighted average of all the possible outcomes
the company will take in 40 with probability of 1
the company will have to pay out 200 with probability of .05
the company will have to pay out 500 with probability of .01
E = 40 - 200(.05) -500(.01)
E = 40 - 10 - 5
E = 25
Therefore for each warranty sold the company can expect a profit of $25.
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10)Chebychev’s inequality:
P(|X-u|>k*s) < 1/k^2
u = mean
s = standard deviation
k>0
In this case u is 100, s is 15.
|130-100| = |70-100| = 30
30 = 2*15, therefore exactly 2 deviations away
k = 2
P(|X-100|>30) < 1/4
1 - 1/4 = 3/4
Therefore
P(|X-100|<30| > 3/4
In other words the probability that X is within 70 and 130 is greater than 3/4
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