SOLUTION: An oil well drilling company generally drills four wells per month. The probability distribution of successful attempts out of the four wells is given by (Table): No. of succes

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Question 1053131: An oil well drilling company generally drills four wells per month. The probability distribution of successful attempts out of the four wells is given by
(Table):
No. of successes (x) 0 1 2 3 4
Probability of successes f(x) 0.1 0.4 0.3 0.1 0.1
Find the expected number of successful wells and the standard deviation. Construct the interval µ ± 2σ and give an interpretation using Chebyshevs theorem.
Answer by Boreal(15235) About Me  (Show Source):
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No. of successes (x) ======0= 1== 2= 3== 4
Probability of successes f(x) 0.1 0.4 0.3 0.1 0.1
E(x)=x(p(x))
=0+0.4+0.6+0.3+0.4=1.7 ANSWER
V(x)= sum p(x) (x-mean)^2
-1.7^2*0+-0.7^2*0.4+0.3^2*0.3+1.3^2*0.1+2.3^2*0.1
=0+0.196+0.027+0.169+0.529=0.921
SD=sqrt(0.921)=0.960 ANSWER
mean +/- 2 sd=2.1+/-1.92 or 1.92; (-0.22,3.62) or (0.3.62) to conform with reality
Using Chebyshev"s Theorem, at least 3/4 of the data lie within this interval. Here, 9 do, with only 4 successes being the outlier. This is consistent.