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In a binomial distribuiton n=6 and pi=.26 x=3 x<3 x>4

In a binomial distribuiton n=6 and pi=.26 x=3 x<3 x>4

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Answer #1

Sample size , n =    6
Probability of an event of interest, p =   0.26
it is a binomial probability distribution,  
  
and probability is given by  

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

a)

P ( X =    3   ) = C(   6   ,   3   )*   0.26   ^   3   *   0.74   ^   3 = 0.1424
b)

P(X<3) =P(x=0)+P(x=1)+P(x=2) =   C(6,x)*0.26x*(1-0.26)(6-x) = 0.8144

c)

P(X>4) = 1-P(x<3)-P(x=3)-P(x=4) = 1 - 0.1424 - 0.8144 - C(   6   ,   4   )*   0.26   ^   4   *   0.74   ^   2 = 1 - 0.1424 - 0.8144 -0.0375 = 0.0056

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