Question

B(16, p) and E(X) = 12.8, then the
27. If X
If X –
standard deviation of X is
(A) 256
(B) 16
(C) 2.56
(D) 1.6​

Answer 1

Answer:

in this question

256 + 23 is required value of X 16 - 67

1.6 value is y (_) X

Answer 2

Concept Introduction:-

The standard deviation measures how far the members of a group vary from the group mean.

Given Information:-

We have been given that If $X -B(16, p)$ and $E(X) = 12.8$.

To Find:-

We have to find that the value of standard deviation of $X$.

Solution:-

According to the problem

In the given Binomial Distribution,

Number of trials, $\mathrm{n}=16$

Let probability of success $=p$

Mean $=E(x)=12.8$

$\Rightarrow \mathrm{np}=12.8\\16p=12.8\\\mathrm{p}=\frac{12.8}{16}\\\mathrm{p}=\frac{4}{5}$

Then probability of failure, $q=1-p=\frac{1}{5}$

Standard deviation for Binomial Distribution $=\sqrt{n p q}$

$=\sqrt{16 \times \frac{4}{5} \times \frac{1}{5}}\\=2.56$

Final Answer:-

The value of standard deviation is $2.56$, so option (c) $2.56$ is correct option.