The famous motion picture Harry Potter and the Sorcerer's Stone shattered the box office debut record previously held by named The Lost World: Jurassic Park (The Wall Street Journal. November 19, 2001). A sample of 100 movie theatres showed that the mean three-day weekend gross was $25,467 per theatre. The sample standard deviation was $4980.

(a) What is the margin of error for this study? Use 95% confidence.

(b) What is the 95% confidence interval estimate for the population mean weekend gross per theatre?

(c) The Lost World took in $72.1 million in its first three-day weekend. Harry Potter and the Sorcerer's Stone was shown in 3672 theatres. What is the 95% confidence interval estimate for the total Harry Potter and the Sorcerer's Stone took in during its first three-day weekend?

(d)An Associated Press article claimed Harry Potter "shattered" the box office debut record held by The Lost World. Do your results agree with this claim?