“Tongue Piercing May Speed Tooth Loss, Researchers Say” is the headline of an article that appeared in the San Luis Obispo Tribune (June 5, 2002). The article describes a study of 52 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 18 of the participants. Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. What assumptions must be made for use of the z confidence interval to be appropriate?