A poll result shows that among 150 randomly selected adults, 57 approved the job of the president of United States.

(a) Can we say that exactly 38% of Americans approved the job of the president?Explain briefly.

(b) Determine the 95% confidence interval for the approval rate of the president's job in United States.

(c) Suppose 400 adults are randomly selected and interviewed, and 38% of them approved the president's job. Determine the 95% confidence interval of the approval rate.

(d) Suppose 1,000 adults are randomly selected and interviewed, and 38% of them approved the president's job. Determine the 95% confidence interval of the approval rate.

(e) If you wish to reduce the size of the 95% confidence interval to 4% or less (i.e., 38%2% or smaller), at least how many people should be interviewed? Describe how you got your answer, clearly and concisely.