Question

In a Binominal distribution, The probability of getting success is \(\frac{1}{5}\) and standard deviation is 4. then its mean is

• A. 20
• B. 25
• C. 100
• D. 12

Answer 1

The Correct Option is A

In a binomial distribution, the mean (\(\mu\)) is given by the formula:

\[\mu = n \cdot p\]

where \(n\) is the number of trials, and \(p\) is the probability of success.

Additionally, the standard deviation (\(\sigma\)) in a binomial distribution is:

\[\sigma = \sqrt{n \cdot p \cdot (1-p)}\]

We are given that \(p = \frac{1}{5}\) and \(\sigma = 4\).

We need to first find \(n\) using the given standard deviation:

\[4 = \sqrt{n \cdot \frac{1}{5} \cdot \left(1 - \frac{1}{5}\right)}\]

Simplify the expression inside the square root:

\[4 = \sqrt{n \cdot \frac{1}{5} \cdot \frac{4}{5}}\]

\[4 = \sqrt{\frac{4n}{25}}\]

Squaring both sides to remove the square root:

\[16 = \frac{4n}{25}\]

Multiply both sides by 25 to isolate the term with \(n\):

\[400 = 4n\]

Divide both sides by 4 to solve for \(n\):

\[n = 100\]

Now, substitute \(n\) and \(p\) back into the formula for mean:

\[\mu = 100 \cdot \frac{1}{5}\]

Simplify:

\[\mu = 20\]

Therefore, the mean of the distribution is 20.