In a binomial distribution $n = 200, p = 0.04$ . Taking Poisson distribution as an approximation to the binomial distribution .
Assertion (A) :- Mean of the Poisson distribution $= 8$
Reason (R) : In a Poisson distribution, $P (X = 4) = \frac{512}{3 e^{8}}$

both A and R are true and R is the correct explanation of A

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both A and R are true and R is not correct explanation of A

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A is true but R is false

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A is false but R is true

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Solution

The correct option is C both A and R are true and R is not correct explanation of A
mean of P.D. $= n p = 8$
And $P (X = 4) = \frac{e^{- 8} (8)^{4}}{4!} = \frac{512}{3 e^{8}}$
Hence both statement are correct but they are not related to each other.

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Similar questions

Q. Assertion (A)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.
Reason (R)
Mean, median and mode of a frequency distribution are related as:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Assertion-and-Reason Type

Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) I f t h e m e d i a n a n d m o d e o f a & M e a n, m e d i a n a n d m o d e o f a f r e q u e n c y d i s t r i b u t i o n a r e 150 a n d & f r e q u e n c y d i s t r i b u t i o n a r e r e l a t e d a s : 154 r e s p e c t i v e l y, t h e n i t s m e a n i s 148. & m o d e = 3 m e d i a n - 2 m e a n . \end{matrix}$

The correct answer is :(a)/(b)/(c)/(d).

Q. Assertion [A]: Ocean temperature remains constant beyond the depth of 1000 m.

Reason [R]: Vertical distribution of temperature in the deep ocean is controlled by density driven water movements.

Read the above given statements and select the option that is true.

Assertion (A): Electrophilic substitution reactions takes place in phenol than in nitro benzene

Reason (R): Hydrogen bonding is present in phenol but not in nitrobenzene

Q. Assertion (A)
Consider the following frequency distribution:

Class interval	3-6	6-9	9-12	12-15	15-18	18-21
Frequency	2	5	21	23	10	12

The mode of the above data is 12.4.

Reason (R)
The value of the variable which occurs most often is the mode.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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In a binomial distribution n=200,p=0.04. Taking Poisson distribution as an approximation to the binomial distribution .Assertion (A) :- Mean of the Poisson distribution =8Reason (R) : In a Poisson distribution, P(X=4)=5123e8

The correct option is C both A and R are true and R is not correct explanation of Amean of P.D. =np=8And P(X=4)=e−8(8)44!=5123e8Hence both statement are correct but they are not related to each other.

In a binomial distribution $n = 200, p = 0.04$ . Taking Poisson distribution as an approximation to the binomial distribution .
Assertion (A) :- Mean of the Poisson distribution $= 8$
Reason (R) : In a Poisson distribution, $P (X = 4) = \frac{512}{3 e^{8}}$

The correct option is C both A and R are true and R is not correct explanation of A
mean of P.D. $= n p = 8$
And $P (X = 4) = \frac{e^{- 8} (8)^{4}}{4!} = \frac{512}{3 e^{8}}$
Hence both statement are correct but they are not related to each other.