To find $P(X < -2)$, we sum the probabilities associated with the values of $X$ that are less than $-2$.

From the given dataTo find $P(X < -2)$, we sum the probabilities associated with the values of $X$ that are less than $-2$.

From the given

$x = -4, -3, -2, -1, 0$ $P(X = -4) = 0.3, \quad P(X = -3) = 0.1, \quad P(X = -2) = 0.1, \quad P(X = -1) = 0.3, \quad P(X = 0) = 0.2$

We are interested in $P(X < -2)$, which means:

$P(X < -2) = P(X = -4) + P(X = -3)$

So:

$P(X < -2) = 0.3 + 0.1 = 0.4$

Thus:

$P(X < -2) = 0.4$

Since the question asks for the answer rounded to one decimal place, the final answer is:

$\boxed{0.4}$

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Do you have any further questions?

Here are five related questions you might find interesting:

1. How would the answer change if the probability of $P(X = -3)$ was 0.2?
2. What is $P(X \leq -2)$?
3. How do we compute $P(X > -1)$?
4. What is the expected value of $X$ given the probabilities?
5. How does a cumulative distribution function (CDF) relate to questions like $P(X < -2)$?

Tip: Always double-check that the probabilities sum to 1 to ensure the distribution is valid.