Question

Our experiment is to roll 2 dice 900 times. The random variable, X, is the number of times that the two dice add up to either 7 or 11. Find E(X), Var(X), and E(X^2).

Assuming that the Central Limit Theorem applies, AND that the standard deviation is exactly 12.5, AND not bothering with the half-unit correction, find:

P(X>225)

P(X<175)

Answer 1

outcome	X	P(X)
(1,6)(6,1)(2,5)(5,2)(3,4)(4,3)	7	6/36
(5,6)(6,5)	11	2/36

P(7 or 11) = 8/36 = 2/9

E(X)= Mean = np =    900*2/9=       200
V(x) = Variance = np(1-p) =    900*2/9*(1-2/9)=       155.5556

E(X2 )=Var(X)+(E(X))2 =155.5556+2002 =40155.56

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P(X >   225   )      
              
Z=(X - µ ) / σ =        (225-200)/12.5)=       2.000
              
=P(Z >   2.000   ) =    0.0228  
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P(X ≤   175   )      
              
Z=(X - µ ) / σ =        (175-200)/12.5)=       -2.000
              
=P(Z≤   -2.000   ) = 0.0228