Question

The mean and standard deviation of a Binomial distribution are 25 and 3 respectively.The number of trials is…

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

Mean of Binomial Distribution = 25

and

Standard deviation of Binomial Distribution = 3

We know,

In Binomial Distribution, consisting of 'n' number of independent trial,

$\rm :\longmapsto\:Mean = np$

and

$\rm :\longmapsto\:Standard \: Deviation \: = \sqrt{npq}$

where,

p is probability of success

q is probability of failure

p + q = 1

Now,

According to statement,

Mean of Binomial Distribution = 25

$\rm :\longmapsto\:np = 25 - - - - (i)$

and

Standard deviation of Binomial Distribution = 3

$\rm :\longmapsto\: \sqrt{npq} = 3$

On squaring both sides, we have

$\rm :\longmapsto\:npq = 9$

On substitute the value of np from (i),

$\rm :\longmapsto\:25q = 9$

$\rm :\longmapsto\:q = \dfrac{9}{25}$

Now,

$\rm :\longmapsto\:p + q = 1$

$\rm :\longmapsto\:p + \dfrac{9}{25} = 1$

$\rm :\longmapsto\:p = 1 - \dfrac{9}{25}$

$\rm :\longmapsto\:p = \dfrac{25 - 9}{25}$

$\rm :\longmapsto\:p = \dfrac{16}{25}$

On substitute the value of p, in equation (i),

$\rm :\longmapsto\:np = 25$

$\rm :\longmapsto\:n \times \dfrac{16}{25} = 25$

$\bf\implies \:n = \dfrac{625}{16} \: which \: is \: not \: natural \: number$

Hence, the value of n for this data, doesn't exist.

Answer 2

Answer:

The number of trials in binomial distribution does not exist

Step-by-step explanation:

Given: The mean of the binomial distribution is 25

The standard deviation of binomial distribution is 3

To find: The number of trials in binomial distribution

Solution:

Mean = np

Standard deviation = $\sqrt{npq}$

n = number of trials

P = probability of success

Mean np = 25

standard deviation

$\sqrt{npq}$ = 3

Variance = $o^{2}$ = $(3)^{2}$

$o^{2}$ = 9

⇒ 9 = np(1-p)

⇒ 9 =25(1 - p)

⇒ 1-p = $\frac{9}{25}$

⇒ $1 - \frac{9}{25}$ = p

⇒ p = $\frac{25 - 9}{25}$

⇒ p = $\frac{16}{25}$

np = 25

n = 25 × 25/16

n = 625 / 16

Where the n value does not exist

Final answer:

The number of trials in binomial distribution does not exist

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