Answer :
Final answer:
The corresponding z-score for the 92% confidence interval is most likely 1.75, option d. It lies between the z-scores for 90% (1.645) and 95% (1.96) confidence intervals provided in examples.
Explanation:
The question asks about the corresponding z-score for the confidence interval of 92%. To find this, we use the concept of the standard normal distribution and z-scores associated with specific confidence levels. The values given in the examples provide the z-scores for the confidence intervals: 68%, 95%, and 99.7%.
Since we do not have a direct example for 92%, we would typically use a z-table or statistical software to determine the exact z-score. However, we can infer that it will lie between the z-scores of the 90% and 95% confidence intervals, which are 1.645 and 1.96, respectively. Hence, we need a value between 1.645 and 1.96.
Considering the options available, the correct z-score that corresponds to a 92% confidence interval, which lies between the z-scores for 90% and 95% confidence levels, must be d. 1.75.
It's worth noting that these z-scores represent the critical values that are used to construct the confidence interval for a population mean or proportion when the population standard deviation is known and the distribution of the sample mean is normally distributed, or the sample size is large enough to apply the central limit theorem.
