From its founding through 2012, the Rock and Roll Hall of Fame has inducted 273 groups or individuals, and 181 of the inductees have been performers while the rest have been related to the world of music in some way other than as a performer. The full dataset is available in Rock and Roll.
(a) What proportion of inductees have been performers? Use the correct notation with your answer.
(b) If we took many samples of size 50 from the population of all inductees and recorded the proportion who were performers for each sample, what shape do we expect the distribution of sample proportions to have? Where do we expect it to be centered?