What is the confidence level of each of the following confidence intervals for $\mu$ ? Complete parts a thro E Click the icon to view the table of normal curve areas. a. $\bar{x} \pm 1.96\left(\frac{\sigma}{\sqrt{n}}\right)$ $95 \%$ (Round to two decimal places as needed.) b. $\bar{x} \pm 1.645\left(\frac{\sigma}{\sqrt{n}}\right)$ $90 \%$ (Round to two decimal places as needed.) c. $\bar{x} \pm 2.575\left(\frac{\sigma}{\sqrt{n}}\right)$ $\%$ (Round to two decimal places as needed.)

Step 1 ：The question is asking for the confidence level of the given confidence intervals for the population mean \(\mu\). The confidence level is determined by the z-score in the confidence interval formula. The z-score corresponds to the area under the normal curve.

Step 2 ：For part c, the z-score is 2.575. We need to find the area under the normal curve that corresponds to this z-score. This area represents the confidence level.

Step 3 ：We can use the scipy.stats.norm library in Python to find the area under the curve for a given z-score. The function norm.cdf(z) gives the area under the curve to the left of the z-score. Since we want the area in both tails of the distribution, we need to subtract the area to the left of -z from the area to the left of z, and then multiply by 100 to get the confidence level as a percentage.

Step 4 ：The confidence level for the interval \(\bar{x} \pm 2.575\left(\frac{\sigma}{\sqrt{n}}\right)\) is approximately 99.00%. This means that we can be 99.00% confident that the population mean \(\mu\) lies within this interval.

Step 5 ：Final Answer: The confidence level for the interval \(\bar{x} \pm 2.575\left(\frac{\sigma}{\sqrt{n}}\right)\) is \(\boxed{99.00\%}\).