Question

Find out the fallacy if any in the statement:

“The mean and the variance of a binomial distribution is 16.2 and 29.4 respectively.”

1. \(q=\dfrac{49}{27}\) is not possible.
2. The statement is true.
3. \(p=\dfrac{47}{27}\) is not possible.
4. \(p=\dfrac{49}{27}\) is not possible.

Answer 1

Correct Answer - Option 1 : \(q=\dfrac{49}{27}\) is not possible.

Given:

Mean (np) = 16.2                        

Variance (npq) = 29.4  

Formula used: 

The mean of a binomial distribution (μ) = np 

Variance of a binomial distribution (σ²) = npq

Where,

p = probability of success,

q = probability of failure

Value of p & q can not be greater then one.

Calculation:

According to question,

np = 16.2                 ........(i)

npq = 29.4               .......(ii)

From equation (I), equation (ii) becomes,

⇒ 16.2 × q = 29.4

\(\Rightarrow q = \frac{294}{162} = \frac{49}{27} > 1\)

Thus, the fallacy is \(q=\dfrac{49}{27}\) is not possible.