Is it possible to have a Binomial distribution with mean 5 and standar

1.	Is it possible to have a Binomial distribution with mean 5 and standarddeviation 3. Verify your answer mathematically
Answer» SOLUTION TO VERIFY Is it possible to have a Binomial distribution with mean 5 and standard deviation 3 EVALUATION Let for the given Binomial distribution two parameters are N , p Then Mean = np $\sf{Standard \: Deviation = \sqrt{npq} }$ Now it is given that the Binomial distribution is with mean 5 and standard deviation 3 So by the given CONDITION $\sf{np = 5 \: \: \: - - - (1)}$ $\sf{ \sqrt{npq} = 3 }$ $\sf{ \implies \: {npq} = 9 }$ $\sf{ \implies \: 5q= 9 }$ $\displaystyle \sf{ \implies \: q= \frac{9}{5} }$ $\displaystyle \sf{ \implies \: 1 - p= \frac{9}{5} }$ $\displaystyle \sf{ \implies \: p= - \frac{4}{5} }$ Which is absurd as probability of an event can not be negative ( 0 ≤ p ≤ 1 ) Hence such Binomial distribution is not possible ━━━━━━━━━━━━━━━━ Learn more from Brainly :- 1. Two dice are thrown together what is the probability number 1 does not appear on both brainly.in/question/6749741 2. AMONG 21 components 3 are DEFECTIVE. what is the probability that a component selected at random is not defective brainly.in/question/22719974

Is it possible to have a Binomial distribution with mean 5 and standarddeviation 3. Verify your answer mathematically

Answer»

TO VERIFY

Is it possible to have a Binomial distribution with mean 5 and standard deviation 3

EVALUATION

Let for the given Binomial distribution two parameters are N , p

Then

Mean = np

$\sf{Standard \: Deviation = \sqrt{npq} }$

Now it is given that the Binomial distribution is with mean 5 and standard deviation 3

So by the given CONDITION

$\sf{np = 5 \: \: \: - - - (1)}$

$\sf{ \sqrt{npq} = 3 }$

$\sf{ \implies \: {npq} = 9 }$

$\sf{ \implies \: 5q= 9 }$

$\displaystyle \sf{ \implies \: q= \frac{9}{5} }$

$\displaystyle \sf{ \implies \: 1 - p= \frac{9}{5} }$

$\displaystyle \sf{ \implies \: p= - \frac{4}{5} }$

Which is absurd as probability of an event can not be negative ( 0 ≤ p ≤ 1 )

Hence such Binomial distribution is not possible

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Learn more from Brainly :-

1. Two dice are thrown together what is the probability number 1 does not appear on both

2. AMONG 21 components 3 are DEFECTIVE. what is the probability that a component selected at random is not defective