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For a given binomial distribution with n = 11, p = 0.35, find the following probabilities...

For a given binomial distribution with n = 11, p = 0.35, find the following probabilities P(x is greater than 7, x> 7)

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Answer #1

)Solution

Given that ,

p = 0.35

q = 1 - p = 1 - 0.35 = 0.65

n = 11

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)- P(X = 7)

= 1 -  (11 C 0) * 0.35 0 * (0.65)11 -  (11 C 1) * 0.35 1 * (0.65)10 -  (11 C 2) * 0.35 2 * (0.65)9 -  (11 C 3) * 0.35 3 * (0.65)8 -  (11 C 4) * 0.35 4 * (0.65)7 -  (11 C 5) * 0.35 5 * (0.65)6 -  (11 C 6) * 0.35 6 * (0.65)4 -  (11 C 7) * 0.35 7 * (0.65)5

= 1 - 0.9878

= 0.0122

Probability = 0.0122

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