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I see the homework problem you're working on. Let's break it down step by step.

The table gives the number of customers per day using credit cards (\(x\)) and their associated probabilities (\(P(x)\)):

| \(x\) (Number of customers) | \(P(x)\) (Probability) |
|-----------------------------|------------------------|
| 8                           | 0.26                   |
| 9                           | 0.01                   |
| 10                          | 0.51                   |
| 11                          | 0.04                   |
| 12                          | 0.18                   |

We need to solve the following:

### a. Find \(P(x < 10)\)
This is asking for the probability that the number of customers is less than 10, i.e., \(P(x = 8) + P(x = 9)\).

From the table:
\[
P(x = 8) = 0.26, \quad P(x = 9) = 0.01
\]
So,
\[
P(x < 10) = P(x = 8) + P(x = 9) = 0.26 + 0.01 = 0.27
\]

### b. Find \(P(x \geq 9)\)
This is asking for the probability that the number of customers is greater than or equal to 9, i.e., \(P(x = 9) + P(x = 10) + P(x = 11) + P(x = 12)\).

From the table:
\[
P(x = 9) = 0.01, \quad P(x = 10) = 0.51, \quad P(x = 11) = 0.04, \quad P(x = 12) = 0.18
\]
So,
\[
P(x \geq 9) = 0.01 + 0.51 + 0.04 + 0.18 = 0.74
\]

### c. Find \(P(8 \leq x < 11)\)
This is asking for the probability that the number of customers is between 8 and 10 (inclusive of 8, exclusive of 11), i.e., \(P(x = 8) + P(x = 9) + P(x = 10)\).

From the table:
\[
P(x = 8) = 0.26, \quad P(x = 9) = 0.01, \quad P(x = 10) = 0.51
\]
So,
\[
P(8 \leq x < 11) = 0.26 + 0.01 + 0.51 = 0.78
\]

Let me know if you'd like further details on any of the steps or need additional clarification.

Here are five related questions to explore further:
1. What is the total probability of all outcomes?
2. How would you calculate the expected value of \(x\)?
3. Can you find the probability of \(x > 10\)?
4. How does the cumulative probability distribution look for this dataset?
5. How would you interpret the standard deviation in this context?

**Tip:** Always check that the total of all probabilities equals 1 to ensure consistency in the table!

Find the probabilities based on a given table of customer usage of credit cards: a) P(x < 10), b) P(x >= 9), and c) P(8 <= x < 11).

Learn how to calculate probabilities based on a table of customer credit card usage. This problem involves finding P(x < 10), P(x >= 9), and P(8 <= x < 11) using basic probability rules. Suitable for students in Grades 9-12.

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