STAT 200 Questions Mind on Statistics 5th Edition Chapter 8 (please provide answ
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Question
STAT 200 Questions Mind on Statistics 5th Edition
Chapter 8 (please provide answers with detailed explanations thank you!)
Burt pays $30 a year for towing insurance. He thinks that the probability that he will need to have his car towed once in the next year is 1/10 and the probability that he will have to have it towed more than once is zero. It will cost $100 if his car is towed if he doesn't have insurance but will cost nothing if he does have insurance. Let X = Burt's cost next year for towing and/or insurance.
a) If Burt buys the insurance, X has only one possible value. What is it?
b) If Burt doesn't buy the insurance, X has two possible values. List the two values and their probabilities.
c) Refer to parts (a) and (b). In each case, find E(X). Using these two values for E(X), explain whether or not Burt should buy the insurance.
Explanation / Answer
A) If Burt buys the insurance, then X can take only one value i.e. 30$, because it doesn't matter whether car would be towed or not.
Case1: Car is towed
It will cost nothing as Burt is paying the insurance, only 30$ would cost him
Case2: Car is not towed
Again, it will not cost nothing
B) In this case we have two possibilities
Case1: Car is towed
It will cost 100$ with the probability 0.1
Case2: Car is not towed
Again, it will not cost 0$ with probability 0.9
C)
Part a): E(X)=Pr(X=30$)*30$=1*30=30$ (As in this case X can take only one value)
Part b) E(X)=Pr(X=100)*0.1 + Pr(X=0)*0.9 =10$
As expected value in part b is less than part a, Burt shouldn't take the insurance.
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