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Let X~B(n,p), if E(X)=5,Var(X)=2.5 then ...

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

A

`((1)/(2))^(11)`

B

`((1)/(2))^(10)`

C

`((1)/(2)))^(6)`

D

`((1)/(2))^(9)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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Knowledge Check

  • Let X ~ B (n, p ), if E (X) = 5, Var (X) = 2.5, then P(X<1) is

    A
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    B
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    D
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    0.1
    B
    0.2
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    D
    0.6

  • For X ~ B (n,p),if E(X) = 18, Var(X) =12, then p =

    A
    `1/3`
    B
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    `3/4`
    D
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