Step 1 :The point estimate is simply the sample proportion, which is 0.85.
Step 2 :The margin of error can be calculated using the formula for the confidence interval of a proportion, which is \( \hat{p} \pm Z \sqrt{(\hat{p}(1-\hat{p}))/n} \), where Z is the Z-score corresponding to the desired level of confidence. For a 90% confidence interval, the Z-score is approximately 1.645.
Step 3 :The confidence interval is then the point estimate plus and minus the margin of error.
Step 4 :Let's calculate the margin of error and the confidence interval. Given values are \( \hat{p} = 0.85 \), \( n = 100 \), and \( Z = 1.645 \).
Step 5 :The margin of error is calculated as \( 0.05873824882476495 \).
Step 6 :The confidence interval is calculated as \( (0.791261751175235, 0.908738248824765) \).
Step 7 :The point estimate for p is 0.85. The margin of error is approximately 0.059, and the 90% confidence interval for p is approximately (0.791, 0.909).
Step 8 :Final Answer: The point estimate is \( \boxed{0.85} \). The margin of error is \( \pm \boxed{0.059} \). The 90% confidence interval is \( \boxed{(0.791, 0.909)} \).