The mean and standard deviation of a random sample of n measurements are equal to 33.8 and 3.2, respectively. a. Find a 90% confidence interval for p if n = 144. b. Find a 90% confidence interval for p if n = 576 c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed? a. The 90% confidence interval for p if n = 144 is approximately (Round to three decimal places as needed.) b. The 90% confidence interval p if n = 576 is approximately (Round to three decimal places as needed.) c. Choose the correct answer below. O A. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 2. O B. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 4. O C. Quadrupling the sample size while holding the confidence coefficient fixed increases the width of the confidence interval by a factor of 4. O D. Quadrupling the sample size while holding the confidence coefficient fixed does not affect the width of the confidence interval. O E. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2