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In this problem, we are given a probability distribution for the variable \( X \), which represents the number of stars given in a restaurant rating system (with 1, 2, 3, 4, or 5 stars). We are asked to calculate two probabilities based on this distribution.

The probability distribution is as follows:

\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Valor } x \text{ de } X & 1 & 2 & 3 & 4 & 5 \\
\hline
P(X = x) & 0.23 & 0.18 & 0.11 & 0.26 & 0.22 \\
\hline
\end{array}
\]

### (a) Menos de 3:
This means we want the probability of getting a rating of less than 3, i.e., \( P(X < 3) \). This corresponds to \( P(X = 1) \) and \( P(X = 2) \). The probability is calculated by summing these values:

\[
P(X < 3) = P(X = 1) + P(X = 2) = 0.23 + 0.18 = 0.41
\]

### (b) 4 o más:
This means we want the probability of getting a rating of 4 or more, i.e., \( P(X \geq 4) \). This corresponds to \( P(X = 4) \) and \( P(X = 5) \). The probability is calculated by summing these values:

\[
P(X \geq 4) = P(X = 4) + P(X = 5) = 0.26 + 0.22 = 0.48
\]

### Final answers:
- (a) \( P(X < 3) = 0.41 \)
- (b) \( P(X \geq 4) = 0.48 \)

Would you like more details on these calculations or have any further questions?

Here are five related questions for deeper understanding:
1. How would you calculate \( P(3 \leq X < 5) \) from this distribution?
2. What is the total probability of all possible outcomes, and why is it always 1?
3. How would the probability distribution change if we added a 6-star rating option?
4. What is the expected value (mean) of the number of stars based on this distribution?
5. How do we calculate the variance of this probability distribution?

**Tip**: When working with probability distributions, the sum of all probabilities should always equal 1. If it doesn't, there might be an error in the data or calculations.

En una aplicación popular, los usuarios califican los restaurantes con 1, 2, 3, 4 o 5 estrellas. Suponga que se selecciona al azar una calificación de todas las calificaciones de la aplicación. Sea X el número de estrellas de la calificación seleccionada. Esta es la distribución de probabilidad de X. ¿Cuál es la probabilidad de que la calificación seleccionada sea menos de 3 o 4 o más?

Learn how to calculate the probability of selecting a specific restaurant rating from a probability distribution. This problem focuses on finding the probability of ratings less than 3 and 4 or more, using basic probability summation. Ideal for high school students studying probability distributions.

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