Let a random variable X have a binomial distribution with mean 8 and variance 4. If P\left ( X\leq 2 \right )=\frac{k}{2^{16}}, then k is equal to : 

 

  • Option 1)

    137

  • Option 2)

    17

  • Option 3)

    121

  • Option 4)

    1

 

Answers (1)

np=8

npq=4

q=\frac{1}{2}\: \: \: \: \: ,\: \: \: n=16

\Rightarrow p=\frac{1}{2}

P\left ( x=r \right )=^{16}C{_{r}}\left ( \frac{1}{2} \right )^{16}

P\left ( x\leq 2 \right )=\frac{16C_{0}+16C_{1}+16C_{2}}{2^{16}}

                      =\frac{137}{2^{16}}

So, the value of k=137


Option 1)

137

Option 2)

17

Option 3)

121

Option 4)

1

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