46. The motion picture Harry Potter and the Sorcerer’s Stone shattered the box office debut record previously held by The Lost World: Jurassic Park (The Wall Street Journal, November 19, 2001). A sample of 100 movie theaters showed that the mean three-day weekend gross was $25,467 per theater. 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 theater?

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 theaters. What is an estimate of 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?