Determine the binomial distribution for which the mean is 20 and … - Vidyadip

Question

Determine the binomial distribution for which the mean is $20$ and variance $16.$

✓

Answer

$n . p = 20,$
$n p q = 16$
$\Rightarrow\text{q}=\frac{16}{20}=\frac{4}{5}\text{ }\text{ }\therefore\text{ }\text{ }\text{p}=\frac{1}{5}\text{and n}=100$
OR The Distribution is $ P(r) = 100_{\text{C}_\text{r}}\Bigg[\frac{4}{5}\Bigg]^\text{100 - r}\cdot\Bigg(\frac{1}{5}\Bigg)^\text{r},\text{ r = 0,1,2,.....,100.}$

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

More "3 Marks Question" from Probability→Probability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

By using the properties of definite integrals, evaluate the integral $\int\limits_{ - 5}^5 {\left| {x + 2} \right|dx} $

Let $A = \{-1, 0, 1, 2\}, B = \{-4, -2, 0, 2\}$ and $f, g : A \rightarrow B$ be the functions defined by $f(x) = x^2 - x, x \in A$ and $g(x) = 2\left| {x - \frac{1}{2}} \right| - 1,x \in A.$ Are $f$ and $g$ equal? Justify your answer. $($Hint: One may note that two functions $f : A \rightarrow B$ and $g : A \rightarrow B$ such that$ f(a) = g(a) \forall$ a $\in A,$ are called equal functions$).$

Evaluate the following:
$\int\frac{\sin\text{x}+\cos\text{x}}{\sqrt{1+\sin2\text{x}}}\text{dx}$

Write the following function in the simplest form:
$\tan^{-1}\bigg(\frac{3a^{2}x-x^{3}}{a^{3}-3ax^{2}}\bigg), a>0; \frac{-a}{\sqrt{3}}\leq x\leq\frac{a}{\sqrt{3}}$

If $\text{y}=\frac{\log\text{x}}{\text{x}},$ show that $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{2\log\text{x}-3}{\text{x}^3}.$

Find the integral of the function $\sin^4 x$

$\overrightarrow{a} = \hat{i} + 2\hat{j} - 3\hat{k}, \overrightarrow{b} = 3\hat{i} - \hat{j} + 2\hat{k}, \text{show that}\bigg(\overrightarrow{a} +\overrightarrow{b}\bigg) \text{and} \bigg(\overrightarrow{a} -\overrightarrow{b}\bigg)$ are perpendicular to each other.

A particle moves along the curve $y = x^3.$ Find the points on the curve at which the $y-$coordinate changes three times more rapidly than the $x-$coordinate.

Integrate the function: $\frac{{2\cos x - 3\sin x}}{{6\cos x + 4\sin x}}$

If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?