To calculate the standard deviation of a binomial random variable $X$, we use the formula:

$\text{Standard Deviation} = \sigma_X = \sqrt{n \cdot p \cdot (1 - p)}$

Where:

• $n = 16$ (the number of trials)
• $p = 0.1$ (the probability of success)

Let's substitute the values:

$\sigma_X = \sqrt{16 \cdot 0.1 \cdot (1 - 0.1)} = \sqrt{16 \cdot 0.1 \cdot 0.9}$ $\sigma_X = \sqrt{16 \cdot 0.09} = \sqrt{1.44} = 1.2$

So, the standard deviation of $X$ is 1.2.

Would you like to go over more details or need help with something else?

Here are some follow-up questions:

1. What is the mean of the binomial distribution for this problem?
2. How would the standard deviation change if $p$ were 0.5?
3. What is the probability of getting exactly 3 successes in 16 trials with $p = 0.1$?
4. How do you calculate the variance for a binomial random variable?
5. How would you interpret the standard deviation in the context of this binomial distribution?

Tip: The standard deviation provides a measure of how spread out the outcomes of a binomial distribution are around the mean. The higher the probability of success, the larger the standard deviation will be.