Find the critical value zc necessary to form a confidence interval at the given level of confidence.
a. 90% = 1.645
b. 85% = 1.8025
90% is correct!
85% is incorrect. Try again.
To find the critical value zc necessary to form a confidence interval at a given level of confidence, we can use the z-table or the standard normal distribution.
a. For a 90% confidence level, we need to find the z-score that leaves 5% in each tail of the normal distribution. Using the z-table, we can find that the z-score for a cumulative area of 0.95 (1 - 0.05) is approximately 1.645. Therefore, the critical value zc for a 90% confidence level is 1.645.
b. For an 85% confidence level, we need to find the z-score that leaves 7.5% in each tail of the normal distribution. Using the z-table, we can find that the z-score for a cumulative area of 0.925 (0.5 + 0.425) is approximately 1.8025. Therefore, the critical value zc for an 85% confidence level is 1.8025.
Using the z-table or a statistical software, we can find the precise values for different confidence levels.
a. To find the critical value zc for a 90% confidence level, we need to use the standard normal distribution table or a calculator.
Using the standard normal distribution table, we look for the area/probability of 0.95 (since we want a 90% confidence level, which means there will be 5% of the data remaining outside the confidence interval).
We find that the z-value corresponding to an area of 0.95 is approximately 1.645. Therefore, for a 90% confidence level, the critical value zc is 1.645.
b. To find the critical value zc for an 85% confidence level, we do the same process. We look for the area/probability of 0.925 (since we want an 85% confidence level, which means there will be 7.5% of the data remaining outside the confidence interval).
We find that the z-value corresponding to an area of 0.925 is approximately 1.8025. Therefore, for an 85% confidence level, the critical value zc is 1.8025.