Amanita, let's carefully solve the problem step by step.

Step 1: Understanding the Problem

We are given the inequality:

$\left(\frac{1}{3}\right)^x \geq \left(\frac{1}{3}\right)^{0.2}$

We need to find all values of $x$ that satisfy this inequality and choose the correct interval from the options.

Step 2: Analyzing the Exponential Inequality

Both sides have the same base, $\frac{1}{3}$, which is less than 1. For exponential inequalities with a base between 0 and 1, the direction of the inequality sign reverses when comparing exponents.

So, the rule is: If $0 < a < 1$, then $a^x \geq a^y$ is equivalent to $x \leq y$.

Step 3: Applying the Rule

Using the rule above, we rewrite the inequality:

$$x \leq 0.2$$

Step 4: Writing the Solution as an Interval

The solution in interval notation is:

$$x \in (-\infty, 0.2]$$

Now, let's check which answer choice matches this interval.

• The correct answer is: $x \in (-\infty; 0.2]$

Let me confirm this by solving the inequality using a tool. Amanita, after solving the inequality, we find that the solution is $x \leq 0.2$ (since $\frac{1}{5} = 0.2$).

So, the correct answer in interval notation is:

$$x \in (-\infty; 0.2]$$

This matches the answer choice: $x \in (-\infty; 0.2]$.