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Let's break down the problem from the image you've uploaded:

### Problem Description:
Rambabu operates a canoe rental service and leases 15 canoes. He has recorded the daily demand for canoes over the past 20 days as shown in the table:

| Daily Demand | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|--------------|----|----|----|----|----|----|----|----|----|----|----|
| Frequency    | 1  | 1  | 2  | 2  | 2  | 3  | 3  | 2  | 1  | 1  | 1  |

We need to:
1. **Calculate the cumulative probability** for demand less than 14 canoes.
2. **Determine the appropriate number of canoes Rambabu should lease**.

### Question 9: 
**What is the cumulative probability P(d < 14) for daily demand of 14 canoes?**

To calculate this, we first sum the frequencies for demands less than 14:
- Demand 10: Frequency = 1
- Demand 11: Frequency = 1
- Demand 12: Frequency = 2
- Demand 13: Frequency = 2

Total frequency for demand < 14 = \( 1 + 1 + 2 + 2 = 6 \)

The total number of observations (total frequency) is 20. Therefore, the cumulative probability is:

\[
P(d < 14) = \frac{6}{20} = 0.30
\]

So, the answer is **c. 0.30**.

### Question 10:
**What is the appropriate number of canoes Rambabu should lease?**

The goal is to find a balance between meeting the demand and minimizing shortages. The demand frequencies suggest that 15 canoes are rented most frequently (3 times), and demand higher than 15 occurs less frequently (at 3 + 2 + 1 + 1 + 1 = 8 days). Since Rambabu currently leases 15 canoes, this seems reasonable based on the distribution. Hence, **15 canoes** is the appropriate number.

So, the answer is **b. 15**.

---

Do you have any further questions or would you like additional details?

### Follow-up Questions:
1. How would the answer change if the total frequency was 30 instead of 20?
2. What would the cumulative probability be for demand less than 16 canoes?
3. How can Rambabu minimize his costs while ensuring he doesn’t lose potential customers?
4. What is the probability of a demand of 17 canoes or higher?
5. How would the answer change if the distribution of demand was more skewed towards higher numbers?

### Tip:
When calculating probabilities, always ensure the total frequency is correctly calculated to avoid small mistakes.

What is the cumulative probability P(d < x) for daily demand of 14 canoes and what is the appropriate number of canoes Rambabu should lease?

Explore the cumulative probability for daily canoe demand less than 14, based on Rambabu's rental service data. Learn how to calculate probability and determine the optimal number of canoes to lease using demand frequency distribution. Suitable for Grades 10-12 students.

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