Cruise Ship Safety: Fun Facts about USCG!

(a) Are the normal conditions and 10% condition met in this case? Justify your answer.

Justifying the answers to the normal conditions and 10% condition for this case.

Answer:

a. Explaining the normal and 10% conditions in this case.

The United States Coast Guard (USCG) plays a vital role in ensuring cruise ship safety. In one particular instance, USCG officers randomly selected passengers for an additional security check before boarding. The total number of passengers on board was 4300, with 1200 in balcony cabins and 2100 in ocean view rooms. An SRS of 1000 passengers was chosen for screening, and let p ^ represent the proportion of passengers in balcony cabins in the sample.

a. The normal condition, which requires np >= 10 and n(1-p) >= 10, is satisfied in this case with n = 1000 and p = 1200/4300.

b. The 10% condition, where n <= 10% of N, holds true with n = 1000 and N = 4300, meeting the criteria for a valid statistical analysis.