A biologist measured the lengths of hundreds of cuckoo bird eggs. Use the relative frequency distribution below to answer the questions that follow.
Lengths of Cuckoo Bird Eggs
Length (in millimeters)	Percent of eggs
18.75–19.75	0.8
19.75–20.75	4.0
20.75–21.75	17.3
21.75–22.75	37.9
22.75–23.75	28.5
23.75–24.75	10.7
24.75–25.75	0.8

Given the relative frequency distribution for the lengths of cuckoo bird eggs, you can analyze the data to answer various statistical questions. Let's break down the key information and use it to address possible queries:

### 1. **Which length interval has the highest frequency of cuckoo bird eggs?**
   - The length interval **21.75–22.75 millimeters** has the highest frequency, with **37.9%** of the eggs falling into this range.

### 2. **What is the cumulative frequency for eggs measuring up to 22.75 millimeters?**
   - To find the cumulative frequency for eggs measuring up to 22.75 millimeters, sum the percentages for all intervals up to and including 21.75–22.75:
     \[
     0.8\% + 4.0\% + 17.3\% + 37.9\% = 60.0\%
     \]
     Therefore, **60.0%** of the eggs are 22.75 millimeters or shorter.

### 3. **What proportion of the eggs are longer than 23.75 millimeters?**
   - To find this, add up the percentages for the intervals that start from 23.75 millimeters onwards:
     \[
     10.7\% + 0.8\% = 11.5\%
     \]
     Thus, **11.5%** of the eggs are longer than 23.75 millimeters.

### 4. **What is the probability that a randomly selected egg is between 20.75 and 23.75 millimeters long?**
   - Add the percentages for the intervals within this range:
     \[
     17.3\% + 37.9\% + 28.5\% = 83.7\%
     \]
     The probability is **83.7%**.

### 5. **Is it more likely for an egg to be less than 21.75 millimeters or more than 24.75 millimeters?**
   - For eggs less than 21.75 millimeters, sum the first three intervals:
     \[
     0.8\% + 4.0\% + 17.3\% = 22.1\%
     \]
   - For eggs more than 24.75 millimeters, sum the last interval:
     \[
     0.8\%
     \]
   - It is more likely for an egg to be less than 21.75 millimeters (**22.1%**) than more than 24.75 millimeters (**0.8%**).

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Do you need further details or have any additional questions?

### Related Questions:
1. What is the mean length of the cuckoo bird eggs if we assume a uniform distribution within each interval?
2. How would the median length of the cuckoo bird eggs be estimated from this data?
3. What is the variance and standard deviation of the egg lengths?
4. How does the relative frequency distribution compare to a normal distribution?
5. What is the interquartile range (IQR) for the egg lengths?

### Tip:
When dealing with frequency distributions, visualizing the data with a histogram can make it easier to identify patterns and tendencies in the data.

Explore the relative frequency distribution of cuckoo bird egg lengths and learn statistical insights. Answer questions such as which length interval has the highest frequency, cumulative frequency analysis, and probability calculations. Suitable for students studying statistics and probability in Grades 10-12.

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