SOLUTION: The random Variable X has a binomial distribution with n=10 and p= 0.5. Determine the probabilities (a) P(X=5) (b) P(X ≤ 2) (c) P(X ≥ 9)

Algebra ->  Probability-and-statistics -> SOLUTION: The random Variable X has a binomial distribution with n=10 and p= 0.5. Determine the probabilities (a) P(X=5) (b) P(X ≤ 2) (c) P(X ≥ 9)       Log On


   

Question 264613: The random Variable X has a binomial distribution with n=10 and p= 0.5. Determine the probabilities
(a) P(X=5) (b) P(X ≤ 2)

(c) P(X ≥ 9) (d) P( 3 ≤ X < 5)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The random Variable X has a binomial distribution with n=10 and p= 0.5. Determine the probabilities
(a) P(X=5)= 10C5(0.5)^5(0.5)^5 = 252*0.03125*0.03125 = 0.2461...
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(b) P(X <= 2)= P(x=0)+P(x=1)+P(x=2) = 10C0(0.5)^0*(.5)^10 + 10C1(0.5)^1(0.5)^9
+ 10C2(0.5)^2*(0.5)^8 = 0.5^10 + 10*(0.5)^10 + 45*0.0009766
= 0.0009766 + 0.009766 + 0.04395 = 0.05469
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(c) P(X >= 9)= P(x=9) + P(x=10) = 10C9(0.5)^9*0.5^1 + 10C10*0.5^10*0.5^0
= 10(0.0009766) + 1*0.0009766 = 0.009766+0.0009766 = 0.0107
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(d) P( 3<= x < 5)= P(x=3)+P(x=4) = 10C3(0.0009766) + 10C4(0.0009766)
= 120*0.0009766 + 210*0.0009766 = = 0.3223
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Cheers,
Stan H.