A cytogeneticist determined the number of crossover events between two genes in fifty cells and obtained the following data:

Crossover Events

Number of crossovers

Number of occurrences

0

7

1

15

2

14

3

9

4

5

>= 5

4

What is the expected frequency for the last category (x >= 5)? 

To determine the expected frequency for the last category (x ≥ 5), we first need to calculate the total number of crossover events across all categories. Then, we'll estimate the proportion for the \( x \geq 5 \) category using the provided data.

### Step 1: Total Number of Occurrences
From the data, the number of occurrences for each category is:

- 0 crossovers: 7 occurrences
- 1 crossover: 15 occurrences
- 2 crossovers: 14 occurrences
- 3 crossovers: 9 occurrences
- 4 crossovers: 5 occurrences
- \( x \geq 5 \) crossovers: 4 occurrences

The total number of occurrences across all categories is:

\[
7 + 15 + 14 + 9 + 5 + 4 = 54 \text{ occurrences}
\]

### Step 2: Expected Frequency for \( x \geq 5 \)
The expected frequency is calculated as the proportion of occurrences for the \( x \geq 5 \) category:

\[
\text{Expected frequency} = \frac{\text{Number of occurrences for } x \geq 5}{\text{Total occurrences}} = \frac{4}{54}
\]

\[
\text{Expected frequency} \approx 0.0741 \text{ or } 7.41\%
\]

So, the expected frequency for the \( x \geq 5 \) category is approximately **7.41%**.

Would you like more details on this solution? 

Here are 5 related questions to explore further:
1. How do we calculate expected frequency for other categories?
2. What is the significance of crossover events in genetics?
3. How does the distribution of crossovers affect genetic diversity?
4. How would the expected frequency change if the sample size increased?
5. What other statistical methods can be used to analyze crossover events?

**Tip:** Expected frequencies are useful in determining how well observed data fits an assumed distribution, such as in a chi-square test.

A cytogeneticist determined the number of crossover events between two genes in fifty cells and obtained the following data

Learn how to calculate the expected frequency for the category x ≥ 5 crossover events from given genetic data. This problem involves probability, frequency distribution, and proportions, suitable for students in Grades 10-12. It provides a detailed breakdown of crossovers between two genes in fifty cells and computes the expected frequency for crossover events occurring 5 or more times.

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