Given that there are 26 owls in the 65 to
67 cm class, estimate the probability that
an owl, chosen at random is between
63 and 73 cm long.

To estimate the probability that an owl chosen at random is between 63 and 73 cm long, we need to interpret the information provided and assume a few things:

1. There are **26 owls** in the **65 to 67 cm** length class.
2. The problem asks us to estimate the probability that an owl's length is between **63 and 73 cm**.

Assumptions:
- The distribution of owl lengths is relatively uniform within this range.
- We don't have explicit data for other length classes (e.g., 63-65 cm, 67-69 cm), but we can extrapolate from the data given.

Steps to estimate the probability:
1. **Range of Interest**: The range we're interested in is from 63 cm to 73 cm, which is a span of **10 cm**.
2. **Class of Known Data**: The only class provided is from 65 cm to 67 cm, which covers **2 cm** and has **26 owls**.
3. **Extrapolation**: Since the distribution is assumed to be relatively uniform, we can estimate the number of owls in the 10 cm range proportionally.

- The length class from 65 to 67 cm (2 cm) contains 26 owls.
- The length from 63 to 73 cm (10 cm) is 5 times larger than the 2 cm class.

So, the total estimated number of owls in the 10 cm range (63 to 73 cm) is approximately:
\[
26 \times 5 = 130 \text{ owls}
\]

Now, to calculate the probability:
- If we assume the total number of owls is spread across all length classes (or given the data we have, assume all 130 owls fall within the 63-73 cm range), then the **probability** that an owl chosen at random falls between 63 and 73 cm would be **1**, or 100%.

However, if this is only a segment of a larger population of owls, the exact probability depends on the total number of owls in all other classes (data not given here). With the information provided, we are estimating that nearly all owls might fall within this range, so the probability is close to 1.

### Do you need further details or have any questions?

### 5 Related Questions:
1. What are the assumptions behind uniform distribution, and how do they affect probability estimation?
2. How would the probability change if we had information about the total population of owls?
3. How could we estimate the probability if the distribution was not uniform?
4. What statistical methods could be used to model owl lengths more accurately?
5. How do different class widths affect the calculation of probabilities in a dataset?

### Tip:
When estimating probabilities from partial data, it's crucial to check if the assumptions (such as uniformity of distribution) are valid.

Given that there are 26 owls in the 65 to 67 cm class, estimate the probability that an owl, chosen at random, is between 63 and 73 cm long.

Estimate the probability that an owl, chosen at random, is between 63 and 73 cm long using a uniform distribution and extrapolation techniques. The problem assumes a class of 26 owls between 65 and 67 cm, and uses proportional reasoning to extend this to a 10 cm range. Ideal for students in Grades 10-12.

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