The Monterey Bay Aquarium, founded in 1984, is situated on the beautiful coast of Monterey Bay in the historic Cannery Row district. In 1985, the aquarium began a survery program that involved randomly sampling visitors as they exit for the day The survey includes visitor demographic information, use of social media, and opinions on their aquarium visit. In 2015, the survey included 356 visitors over age 65, of which 52 used a mobile device such as an Android phone or iPad during their visit. (a) What is the margin of error m, of the large-sample 95% confidence interval for the proportion of visitors over 65 who used a mobile device during their visit? (Enter your answer rounded to four decimal places.)
(b) How large a sample n, is needed to get the common +-3 percentuge point margin of error? Use the 2015 sample as a pilot study to get p". (Enter your answer as a whole number.)