Final answer:
The sample mean is calculated to be 66.15, option D. The z value for a 96.6% confidence interval would be slightly higher than the z value for a 95% confidence interval, but the precise value cannot be determined without additional data or resources.
Step-by-step explanation:
The student's question pertains to finding the sample mean from a given interval estimate for a population mean and determining the z value for a 96.6% confidence interval. To uncover the sample mean, we need to recognize that the interval estimate is formed around it. Since the interval is symmetric around the sample mean, the mean lies exactly in the middle of the interval estimate of 62.84 to 69.46. The calculation would be (62.84 + 69.46) / 2 = 66.15, so the correct answer is D. 66.15.
As for the z value for a 96.6% confidence interval estimate, this corresponds to a z value that leaves 3.4% (100% - 96.6%) of the probability in the two tails of the standard normal distribution. Since 1.96 is the z value for a 95% confidence interval (which leaves 5% in the two tails), and we are looking for a slightly higher confidence level, we need a z value that is slightly larger than 1.96. Thus, the correct answer is likely to be between option A (1.96) and C (1.82), which makes B (2.00) or D (2.12) the likelier options.