Final answer:
The critical value for a 95% confidence level is approximately ±1.96 according to the standard normal (Z) distribution for a two-tailed test. However, the decision to use the Z-distribution or the t-distribution depends on the sample size and whether the population standard deviation is known.
Step-by-step explanation:
To determine the critical value for a 95% confidence level, we can use the standard normal distribution (Z-distribution) or a t-distribution depending on the information provided about the population standard deviation and the sample size. If the population standard deviation is known and the sample size is large enough, we would use the Z-distribution. The normal table indicates that the critical value for a 95% confidence interval in a two-tailed test is approximately ±1.96, which corresponds to the Z-scores that cut off the outer 5% of the distribution (2.5% in each tail).
Alternatively, if we are dealing with a smaller sample size and the population standard deviation is unknown, we should use the t-distribution with degrees of freedom (df) equal to n - 1. However, the question does not provide enough information to determine whether we should use the Z-distribution or the t-distribution and also does not provide a sample size.