Consider the following data:

x

−4−4

−3−3

−2−2

−1−1

00

P(X=x)�(�=�)

0.30.3

0.10.1

0.10.1

0.30.3

0.20.2

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Step 5 of 5 :

Find the value of P(X<−2)�(�<−2). Round your answer to one decimal place.

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:

\[
\boxed{0.4}
\]

---

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.

Find the value of P(X < −2) given the probability distribution for X. Round your answer to one decimal place.

Learn how to calculate the probability P(X < −2) from a discrete probability distribution table. This step-by-step solution involves summing probabilities associated with values of X less than -2. Suitable for high school students learning probability theory.

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