Questions: Find the critical value za / 2 needed to construct a confidence interval with the given level.

Solution Steps

To find the critical value \( z_{\alpha/2} \) for a given confidence level, we need to determine the z-score that corresponds to the tail area of \(\alpha/2\) in a standard normal distribution. This involves using the inverse of the cumulative distribution function (CDF) for the normal distribution.

The problem states a confidence level of 1.04. However, confidence levels are typically expressed as a percentage less than or equal to 1 (e.g., 0.95 for 95%). A confidence level of 1.04 is not valid because it exceeds 100%.

The value of \(\alpha\) is calculated as: \[ \alpha = 1 - \text{confidence level} \] Given the confidence level of 1.04, we find: \[ \alpha = 1 - 1.04 = -0.04 \] This negative value for \(\alpha\) indicates an error in the confidence level, as \(\alpha\) should be a positive number between 0 and 1.

The critical value \(z_{\alpha/2}\) is typically found using the inverse of the cumulative distribution function (CDF) for the standard normal distribution. However, since \(\alpha\) is negative, the calculation for \(z_{\alpha/2}\) is not possible, resulting in an undefined value.

Final Answer