Final answer:
To calculate an 80% confidence interval for a population mean with a known standard deviation, use a confidence coefficient of 1.282, which corresponds to the z-score that puts 5% in each tail of the standard normal distribution.
Step-by-step explanation:
To calculate an 80% confidence interval for a population mean, you will need to use a confidence coefficient. This coefficient corresponds to the z-value from the standard normal distribution that captures the desired confidence level. For an 80% interval, we target the central 80% of the probability distribution. This means we are leaving 20% in the tails, or 10% in each tail since it's two-sided.
The critical z-values provided for various confidence levels in the question suggest those primarily used for constructing confidence intervals. For an 80% confidence interval, you would choose the z-value that leaves 10% of the distribution in the tails (5% in each tail). Based on the given options, the correct z-value is z_(0.10), which corresponds to a z-score of 1.282. Therefore, for an 80% confidence interval when the population standard deviation is known, use a confidence coefficient of 1.282.