Question

Assume the random variable X has a binomial distribution with the given probability of obtaining success. Find the following probability, given the number of trials and the probability of obtaining success. Round your answer to four decimal places. P(X≥7), n=10, p=0.3

Answer 1

Solution

Given that ,

p = 0.3

q = 1 - p = 1 - 0.3 = 0.7

n = 10

Using binomial probability formula ,

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

P(X 7  ) = 1 - P( x <7)

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

= 1 - (10 C 0) * 0.3 0 * (0.7)10- (10 C 1) * 0.3 1 * (0.7)9- (10 C 2) * 0.3 2 * (0.7)8- (10 C 3) * 0.3 3 * (0.7)7- (10 C 4) * 0.3 4 * (0.7)6- (10 C 5) * 0.3 5 * (0.7)5- (10 C 6) * 0.3 6 * (0.7)4

=1-0.9894

probability=0.0106