This question involves finding critical values and interpreting a confidence level for a sample mean. Here's how to approach it:

1. Confidence Level: The given confidence level is 95%. For a two-tailed test, the significance level, $\alpha$, is $1 - 0.95 = 0.05$.

2. Critical Values:

   • For a two-tailed test, divide $\alpha$ by 2: $\alpha/2 = 0.025$.
   • Use a standard normal table or Z-table to find the critical Z-values corresponding to $\alpha/2 = 0.025$ and $1 - \alpha/2 = 0.975$.
   • The critical Z-values are:
     • Left: $-1.96$
     • Right: $1.96$

These values are consistent for a standard normal distribution (Z-distribution) when dealing with a 95% confidence level.

Would you like:

1. A detailed breakdown of how these values are calculated using a Z-table or calculator?
2. Assistance with entering the values into the system?
3. Help with understanding what the confidence level means in this context?
4. An explanation of how the sample mean ties into this problem?
5. Further examples to practice finding critical values?

Tip: For any normal distribution, memorizing common Z-scores for 90%, 95%, and 99% confidence intervals can save time!