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.
Find the critical value that corresponds to a confidence level of 95%.
The critical value that corresponds to a confidence level of 95% can be found using the standard normal distribution (Z-distribution). This can be done by finding the value of Z from the standard normal distribution table or by using an online calculator.
For a confidence level of 95%, we need to find the critical value associated with an alpha level of 0.05. Since the distribution is symmetric, we can divide this alpha level equally between the two tails of the distribution.
The alpha level for each tail would be (1-0.95)/2 = 0.025.
Looking up the Z-value for an alpha level of 0.025 in the standard normal distribution table or using an online calculator, we find that the critical value is approximately 1.96.
Therefore, the critical value that corresponds to a confidence level of 95% is 1.96.