Final answer:
The z-score for a 97% confidence interval is approximately 2.17, falling between the z-scores for a 95% confidence interval (1.96) and a 99.7% confidence interval (3.00).
Step-by-step explanation:
The z-score that corresponds with a 97% confidence interval is not directly provided in the typical z-tables, but it can be closely estimated using the empirical rule, which is also known as the 68-95-99.7 rule, or more accurately obtained using statistical software or tables that provide more precise values for z-scores. A 97% confidence interval would be slightly less than the 99.7% confidence interval, which corresponds to z-scores of -3 and +3. Therefore, the 97% confidence interval z-score would be between the z-scores for a 95% confidence interval (around 1.96) and those for a 99.7% confidence interval (3).
If more precision is necessary, one might consult more detailed statistical tables or software to find that the exact z-score for a 97% confidence interval would be approximately 2.17. This means that 97% of the y values would fall between -2.17 and +2.17 standard deviations from the mean. The critical value will change depending on the confidence level of the interval.
The appropriate z-score for a 97% confidence interval can be found by subtracting the confidence level from 1 and dividing the result by 2. This is because the confidence interval is split evenly in both tails of the distribution. So, for a 97% confidence interval, we have (1 - 0.97) / 2 = 0.015. Looking up this value in a standard normal distribution table, we find that the z-score is approximately ±2.17.