Question

Suppose X is a binomial random variable, where n=12 and p = 0.4

compute p >= 10

a) 0.00032

b) 0.00661

c) 0.00459

d) 0.00281

Answer 1

Solution

Given that ,

p = 0.4

q = 1 - p = 1 - 0.4 = 0.6

n = 12

Using binomial probability formula ,

P(X = x) = (n C x) * p x * (1 - p)n - x

P(X 10 ) = 1 - P( x <10)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4) - P(X = 0)5- P(X = 6 - P(X = 7) - P(X = 8) - P(X = 9)

= 1 - (12 C 0) * 0.4 0 * (0.6)12 - (12 C 1) * 0.4 1 * (0.6)11 - (12 C 2) * 0.4 2 * (0.6)10 - (12 C 3) * 0.4 3 * (0.6)9 - (12 C 4) * 0.4 4 * (0.6)18 - (12 C 5) * 0.4 5 * (0.6)7 - (12 C 6) * 0.4 6 * (0.6)6 - (12 C 7) * 0.4 7 * (0.6)5 - (12 C 8) * 0.4 8 * (0.6)4 - (12 C 9) * 0.4 9 * (0.6)3 -

=1-0.99719

probability=0.00281