You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 82.8%.
To find the critical value that corresponds to a confidence level of 82.8%, we need to determine the z-score associated with the confidence level.
Since the normal distribution is a reasonable approximation for the binomial distribution in this case, we can use the standard normal distribution (z-distribution) to find the critical value.
First, we find the z value that corresponds to the confidence level of 82.8%. To do this, we look up the area to the left of this Z-value in the standard normal distribution table or use a statistical software.
Using statistical software or a table, the z-value corresponding to the area to the left of 82.8% is approximately 1.386.
Thus, the critical value that corresponds to a confidence level of 82.8% is approximately 1.386.