Compute the following binomial probabilities directly from t

Compute the following binomial probabilities directly from the formula for

b(x; n, p). (Round your answers to three decimal places.)(a)    

b(5; 8, 0.3)

(b)    

b(6; 8, 0.55)

(c)    

P(3 X 5)

when n = 7 and p = 0.65


(d)    

P(1 X)

when n = 9 and p = 0.1

Solution

1) b(5; 8, 0.3)
P( X = 5 ) = ( 8 5 ) * ( 0.3^5) * ( 1 - 0.3 )^3
= 0.0467

2) b(6; 8, 0.55)
P( X = 6 ) = ( 8 6 ) * ( 0.55^6) * ( 1 - 0.55 )^2
= 0.1569

3)
P( X = 3 ) = ( 7 3 ) * ( 0.65^3) * ( 1 - 0.65 )^4
= 0.1442
P( X = 4 ) = ( 7 4 ) * ( 0.65^4) * ( 1 - 0.65 )^3
= 0.2679
P( X = 5 ) = ( 7 5 ) * ( 0.65^5) * ( 1 - 0.65 )^2
= 0.2985

p( 3<=X<=5) = 0.1442 + 0.2679 + 0.2985 = 0.7106

4)
P( X < = 1) = P(X=1) + P(X=0) +   
= ( 9 1 ) * 0.1^1 * ( 1- 0.1 ) ^8 + ( 9 0 ) * 0.1^0 * ( 1- 0.1 ) ^9 +
= 0.7748