with the same question asnwer these ones 
less then 57%
Between 57 and 90
less then 90
Greater then 78

To answer these new questions, let's analyze the box plot you provided earlier with the specific values in mind:

### Recalculated Points Based on the Given Box Plot:
- **Minimum (Lower Whisker)**: 40
- **Lower Quartile (Q1)**: 50
- **Median (Q2)**: 70
- **Upper Quartile (Q3)**: 90
- **Maximum (Upper Whisker)**: 110

### Questions:

1. **Less than 57%**:
   - The 57th percentile is between the median (70) and the first quartile (50). Since the median (70) corresponds to 50% of the data, and Q3 (90) corresponds to 75%, 57% would fall somewhere between 50 and 70. Thus, approximately **slightly more than 50%** of the data is less than 57.

2. **Between 57% and 90%**:
   - 57% lies between the median (70) and the third quartile (90). As the range from Q2 (70) to Q3 (90) corresponds to 25% of the data, and 57% is just above 50%, approximately **between 7% and 25%** of the data falls between 57% and 90%.

3. **Less than 90**:
   - 90 corresponds to the upper quartile (Q3), so 75% of the data is less than 90.

4. **Greater than 78**:
   - 78 falls between the median (70) and Q3 (90), meaning it's in the upper 25% of the data distribution. Approximately **between 10% and 25%** of the data is greater than 78.

### Summarized Answers:
a) Less than 57%: **Slightly more than 50%**  
b) Between 57% and 90%: **Between 7% and 25%**  
c) Less than 90: **75%**  
d) Greater than 78: **Between 10% and 25%**  

Would you like any further explanations or additional questions on this topic?

### Related Questions:
1. How can you determine the exact percentile for a given data point using a box plot?
2. What is the significance of the median in a box plot?
3. How can you visually estimate percentiles on a box plot?
4. Why does the interquartile range represent 50% of the data?
5. How can outliers be identified on a box plot?

### Tip:
When interpreting a box plot, remember that the percentiles (like 57%) aren't directly shown but can be estimated based on the position relative to the quartiles.

Explore detailed solutions to interpreting percentiles and box plots. Learn how to analyze data distributions using statistical concepts such as quartiles and medians. Includes answers to specific questions related to percentile ranges and their interpretations.

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