KShersbeaimar
Answered

Compute the following binomial probabilities directly from the formula for b(x; n, p):

Ab(3; 8, .35)
Bb(5; 8, .6)
CP(3<=X<=5) when n=7 and p = .6
DP(1 <= X) when n=9 and p= .1

Verified Answer :

nobillionaireNobley

b(x; n, p) = nCx(p^x (1 - p)^(n - x))

a.) b(3; 8, .35) = 8C3(0.35^3 0.65^5) = 56 x 0.042875 x 0.116029 = 0.2786

b.) b(5; 8, .6) = 8C5(0.6^5 0.4^3) = 56 x 0.07776 x 0.064 = 0.2787

c.) P(3 <= x <= 5) = P(3) + P(4) + P(5) = 7C3(0.6^3 0.4^4) + 7C4(0.6^4 0.4^3) + 7C5(0.6^5 0.4^2) = (35 x 0.216 x 0.0256) + (35 x 0.1296 x 0.064) + (21 x 0.07776 x 0.16) = 0.193536 + 0.290304 + 0.2612736 = 0.7451

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