12.40 Major Hurricanes. A major hurricane is a category 3, 4, or 5 hurricane on the Saffir/Simpson Hurricane Scale. From the document "The Deadliest, Costliest, and Most Intense United States Tropical Cyclones From 1851 to 2004" (NOAA Technical Memorandum, NWS TPC-4, Updated 2005) by E. Blake et al., we found that of the 273 hurricanes affecting the continental United States, 92 were major.

a. Based on these data, find and interpret a 90% confidence in- terval for the probability, p, that a hurricane affecting the con- tinental United States will be a major hurricane.

b. Discuss the possible problems with this analysis.