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 99.7%.
(Report answer accurate to three decimal places with appropriate rounding.)
The critical value for a confidence level of 99.7% can be found by considering the area outside of the confidence interval. Since the confidence interval is centered around the population proportion, we are interested in the tail areas on both sides of the confidence interval.
Since the confidence level is 99.7%, we need to find the area outside of the confidence interval on both sides, which is (1 - 0.997) / 2 = 0.0015.
Using a standard normal distribution table or a calculator, we can find the z-value corresponding to the area of 0.0015, which is approximately 3.090.
Therefore, the critical value that corresponds to a confidence level of 99.7% is 3.090.