Question

Suppose that X is a binomial random variable with n = 11 and p = 0.28 . Find P( 5 ).

Write only a number as your answer. Round to 4 decimal places (for example 0.1849). Do not write as a percentage.

Answer 1

Solution

Given that ,

p = 0.28

1 - p = 1 - 0.28 = 0.72

n = 11

x = 5

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * p^x * (1 - p)^{n - x}

P(X = 5) = ((11! / 5! (11 - 5)!) * 0.28⁵ * (0.72)^{11 - 5}

= ((11! / 5! (6)!) * 0.28⁵ * (0.72)⁶

= 0.1108

P(5) = 0.1108