Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥7), n=10, p=0.5

Answer 1

Solution

Given that ,

p = 0.5

q = 1 - p = 1 - 0.5 = 0.5

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) * 0.5 0 * (0.5)10 - (10 C 1) * 0.5 1 * (0.5)9 - (10 C 2) * 0.5 2 * (0.5)8 - (10 C 3) * 0.5 3 * (0.5)7 - (10 C 4) * 0.5 4 * (0.5)6 - (10 C 5) * 0.5 5 * (0.5)5 - (10 C 6) * 0.5 6 * (0.5)4

=1-0.8281

probability=0.1719