Inheritance relates to how a child receives genetic information from their parents. A scientist in the mid 19th century, Gregor Mendel, formulated "laws" to understand genetic inheritance, known as Mendel's laws of inheritance.

(a) These laws infer that offspring in a second-generation cross have a 75% chance of carrying a dominant trait and a 25% chance of carrying a recessive trait. Inheritance occurs independently in each individual. What is the sampling distribution of the proportion of dominant traits in a second-generation cross yielding 711 individuals?

(b) A random sample of size n = 39 is obtained from a Normally-distributed population. A researcher will use the sample to test a hypothesis about the population mean. Is the Central Limit Theorem relevant to the conditions for this hypothesis test? Justify your answer.