Question

The distribution of the binomial random variable (X) has the following parameters p = 0.3 and n = 9. Determine standard deviation of X

Answer 1

The standard deviation of a binomial random variable \( X \) can be calculated using the formula:

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

where:
- \( n \) is the number of trials,
- \( p \) is the probability of success in each trial,
- \( \sigma \) is the standard deviation.

Given:
- \( n = 9 \)
- \( p = 0.3 \)

First, calculate \( 1 - p \):

\[
1 - p = 1 - 0.3 = 0.7
\]

Now substitute the values into the standard deviation formula:

\[
\sigma = \sqrt{9 \cdot 0.3 \cdot 0.7}
\]

Calculating the product inside the square root:

\[
9 \cdot 0.3 = 2.7
\]
\[
2.7 \cdot 0.7 = 1.89
\]

Now, take the square root:

\[
\sigma = \sqrt{1.89} \approx 1.374
\]

Thus, the standard deviation of \( X \) is approximately **1.374**.