Compute the following binomial probabilities directly from the formula for b(x; n, p): a.?? (3; 8, .35) b.?? (5; 8, .6) c.P(3 ? X ? 5) when n= 7 and p = .6 d. P(1? X) when n = 9 p = .1

Answer : Step 1 of 4 : Let us consider the binomial distribution n n nx P(X = x) = ( )(p) (x p) x=0 a) The claim is to find B(3, 8,0.35) X~ B(3, 8,0.35) n P(X = x) = ( )(p) (1 p) nx x=0 x Where x = 3, n = 8 and p = 0.35 8 8 3 83 P(X = 3) = ( )(0.353 (1 0.35) x=0 = (56) (0.043) (0.116) = 2.2785 Therefore, B(3, 8,0.35) = 2.2785 Step 2 of 4 : b) The claim is to find B(5, 8,0.6) X~ B(5, 8,0.6) n P(X = x) = ( )(p) (x p) nx x=0 Where x = 5, n = 8 and p = 0.6 8 P(X = 5) = ( )(0.60) (1 0.60) 85 x=0 5 = (56) (0.078) (0.064) = 2.787 Therefore, B(5, 8,0.60) = 2.2787