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
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 = 0) -P(X = 0) -P(X = 0) -P(X = 0) -P(X = 0) -P(X = 0)
= 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) - (10 C 6) * (0.5)6 * (0.5)4
=0.1719
probability=0.1719
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