Final answer:
The z-scores that capture a 95% confidence interval for a normal distribution are approximately ±1.96.
Step-by-step explanation:
The intervals that capture a 95% confidence interval for a normal distribution are determined by the z-scores that cut off the outer 5% of the probability in the tails of the distribution. When constructing a two-sided 95% confidence interval, you divide this 5% evenly between the upper and lower tails, resulting in 2.5% in each tail. The z-score that corresponds to 0.025 in the upper tail is around 1.96.
This means that the z-scores of roughly ±1.96 will capture the middle 95% of the data, making option 3) 1.96 the correct choice. In comparison, a 90% confidence interval would be narrower, as there is less area under the curve being captured. Conversely, a 99% confidence interval would be wider because it aims to capture 99% of the distribution, leaving only 0.5% in each tail, corresponding to a higher z-score than that for the 95% confidence interval.