For $$ C=95 \% $$ If $$ \sigma=7.21 $$ and $$ \mathrm{n}=35 $$ then $$ E=4.12 $$

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UpStudy AI · Accepted Answer

To solve for the margin of error $$ E $$ in a confidence interval, we can use the formula:

$$
E = z \cdot \frac{\sigma}{\sqrt{n}}
$$

where:
- $$ E $$ is the margin of error,
- $$ z $$ is the z-score corresponding to the desired confidence level,
- $$ \sigma $$ is the population standard deviation,
- $$ n $$ is the sample size.

### Step 1: Find the z-score for $$ C = 95\% $$

For a 95% confidence level, the z-score can be found using standard normal distribution tables or calculators. The z-score for a 95% confidence level is approximately $$ z = 1.96 $$.

### Step 2: Substitute the known values into the formula

Given:
- $$ \sigma = 7.21 $$
- $$ n = 35 $$

We can now substitute these values into the formula for $$ E $$:

$$
E = 1.96 \cdot \frac{7.21}{\sqrt{35}}
$$

### Step 3: Calculate $$ \sqrt{n} $$

First, we calculate $$ \sqrt{35} $$:

$$
\sqrt{35} \approx 5.916
$$

### Step 4: Calculate $$ \frac{\sigma}{\sqrt{n}} $$

Now we can calculate $$ \frac{7.21}{\sqrt{35}} $$:

$$
\frac{7.21}{5.916} \approx 1.220
$$

### Step 5: Calculate the margin of error $$ E $$

Now we can calculate $$ E $$:

$$
E = 1.96 \cdot 1.220 \approx 2.392
$$

### Conclusion

The calculated margin of error $$ E $$ is approximately $$ 2.39 $$, which is different from the provided value of $$ 4.12 $$.

If you would like to verify or explore further, please let me know!
The margin of error $$ E $$ is approximately $$ 2.39 $$.

For \( C=95 \% \) If \( \sigma=7.21 \) and \( \mathrm{n}=35 \) then \( E=4.12 \)

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