Final answer:
To construct a 95% confidence interval given n = 480 and p-hat = 0.85, substitute the values into the formula: p-hat ± (Z * sqrt((p-hat * (1 - p-hat)) / n)). The 95% confidence interval is approximately (0.810, 0.874).
Step-by-step explanation:
To construct a 95% confidence interval, we can use the formula:
p-hat ± (Z * sqrt((p-hat * (1 - p-hat)) / n))
Given that n = 480 and p-hat = 0.85, we need to find the critical value Z for a 95% confidence level. Using a standard normal probability table or a calculator function, we find Z = 1.96.
Substituting the values into the formula, we get:
0.85 ± (1.96 * sqrt((0.85 * (1 - 0.85)) / 480))
Simplifying, the 95% confidence interval is approximately (0.810, 0.874).