Two soda companies are running a prize giveaway. Fizzy Cola has placed winning messages under $12\%$ of its bottle caps. Carbalicious has placed winning messages under $20\%$ of its bottle caps. A random sample of $60$ Fizzy Cola bottles will be chosen and the proportion of winning bottle caps will be calculated. The same will be done for $55$ randomly chosen bottles of Carbalicious. The difference between these proportions will then be calculated.
What can be said about the sampling distribution of the difference in proportions of winning caps for the two sodas?