Download App

STD 12 - 13. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. probability4 Marks
Question
Let a random variable $X$ have a binomial distribution with mean $8$ and variance $4$. If $P\left( {X \le 2} \right) = \frac{k}{{{2^{16}}}}$,  then $k$ is equal to
✓

Answer

b
$\mathrm{np}=8$

$\mathrm{npq}=4$

$\mathrm{q}=\frac{1}{2} \Rightarrow \mathrm{p}=\frac{1}{2}$

$n=16$

$p(x=r)=^{16} C_{r}\left(\frac{1}{2}\right)^{16}$

$p(x \leq 2)=\frac{^{16} C_{0}+^{16} C_{1}+^{16} C_{2}}{2^{16}}$

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{-1,0,1\}$. The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A ^{ T } A$ is $6$ is.
→
The series of positive multiples of $3$ is divided into sets : $\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots$ Then the sum of the elements in the $11^{\text {th }}$ set is equal to $................$
→
Let $1, \omega$ and $\omega)^2$ be the cube roots of unity. The least possible degree of a polynomial with real coefficients, having $2 \omega \omega^2, 3+4 \omega, 3+4 \omega^2$ and $5-\omega-\omega^2$ as roots is
→
In the expansion of ${(1 + 3x + 2{x^2})^6}$ the coefficient of ${x^{11}}$ is
→
Consider $10$ observation $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}$. such that $\sum_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. The $\frac{\beta}{\alpha}$ is equal to :
→
Let $\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$ and $\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}$

If $8 x^{2}+b x+c=0$ is a quadratic equation whose roots are $\alpha^{1 / 5}$ and $\beta^{1 / 5}$, then the value of $c-b$ is equal to:

→
Let $f : R \rightarrow R$ be defined as $f ( x )= x ^{3}+ x -5$.

If $g ( x )$ is a function such that $f ( g ( x ))= x$, $\forall x \in R$, then $g ^{\prime}(63)$ is equal to

→
If $f(x)$ satisfies $f(7 -x) = f(7 + x)\ \forall \,x\, \in \,R$ such that $f(x)$ has exactly $5$ real roots which are all distinct such that sum of the real roots is $S$ then $S/7$ is equal to
→
If $f(x) \, \& \,g(x)$ are inverse functions of each other such that $f(1) = 3\, \& \,f(3) = 1,$ then $\int\limits_1^3 {\left( {g(x) + \frac{x}{{f'\left( {g\left( x \right)} \right)}}} \right)} dx$ is equal to -
→
How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$ ?
→