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A random sample of height of hundred during form a lot of a nation of student having a standard deviation of 0.35 show and average height of 1.75 litre but at 95% confidence limit for the average height of a student form in the population?
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A random sample of height of hundred during form a lot of a nation of ...
Understanding Confidence Intervals
Confidence intervals provide a range of values that likely contain the true population parameter. In this case, we're estimating the average height of students based on a sample.

Given Data
- Sample size (n): 100
- Sample mean (x̄): 1.75 meters
- Standard deviation (σ): 0.35 meters
- Confidence level: 95%

Calculating the Confidence Interval
1. **Determine the Z-value**
For a 95% confidence level, the Z-value (critical value) is approximately 1.96.
2. **Calculate the Standard Error (SE)**
The standard error of the mean is calculated using the formula:

SE = σ / √n
SE = 0.35 / √100
SE = 0.35 / 10
SE = 0.035
3. **Compute the Margin of Error (ME)**
The margin of error is found by multiplying the Z-value by the standard error:

ME = Z * SE
ME = 1.96 * 0.035
ME = 0.0686 (approx.)
4. **Determine the Confidence Interval**
The confidence interval is given by:

Lower Limit = x̄ - ME
Upper Limit = x̄ + ME
Lower Limit = 1.75 - 0.0686 ≈ 1.6814
Upper Limit = 1.75 + 0.0686 ≈ 1.8186

Final Result
At a 95% confidence level, the average height of students in the population is estimated to be between approximately **1.6814 meters** and **1.8186 meters**. This means we can be 95% confident that the true average height falls within this range.
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