Let `X~B(n,p)`, if E(X)=5,Var(X)`=2.5` then `P(X lt 1)` is equal to

Options

A. `((1)/(2))^(11)`
B. `((1)/(2))^(10)`
C. `((1)/(2)))^(6)`
D. `((1)/(2))^(9)`

Answer

B

Explanation

Given mean E(x)=5 and variance, Var(X)=2.5
`therefore np=5 and npq=2.5`
`Rightarrow 5q=2.5=q=(1)/(2)`
Also, p+q=1
`therefore p=1-(1)/(2)=(1)/(2)`
`therefore np=5`
`Rightarrow np=5`
`Rightarrow n xx(1)/(2)=5 " "[therefore p=(1)/(2)]`
`Rightarrow n=10`
`p(X lt 1)==p(X=0)=""^(n)C_(r) p^(r) q^(n-r)`
`=""^(10)C_(0) ((1)/(2))^(0) ((1)/(2))^(10-0)`
`=1xx 1xx((1)/(2))^(10)=((1)/(2))^(10)`