Question

Find each (Z_{a/2}) for the following confidence intervals:

a. (Z_{a/2}) for the 99% confidence interval
a. 1.96
b. 2.33
c. 2.58
d. 2.81

Answer 1

To find the Za/2 for a 99% confidence interval, we determine the z-score that leaves 0.5% in the upper tail, which is approximately 2.58, making c. 2.58 the correct answer.

Step-by-step explanation:

The question is asking to find the critical value (Za/2) for a 99% confidence interval. To find critical values, we reference the standard normal distribution that corresponds to the tails of the distribution given a certain confidence level. A 99% confidence interval suggests we want the central 99% of the distribution, leaving 1% in the tails. Thus, the area in each tail is 0.5% or 0.005.

To obtain Za/2 for a 99% confidence interval, we look for the z-score that leaves 0.005 in the upper tail. Looking up this area in the standard normal distribution table or using statistical software gives us a z-score of approximately 2.58.

Therefore, the answer is c. 2.58, which is the z-score for the 99% confidence interval. The other options do not correspond to the correct critical value for this level of confidence.