7.12 Gender distributions At a university, 60% of the 7,400 students are female. The student newspaper reports results of a survey of a random sample of 50 students about various topics involving alcohol abuse, such as participation in binge drinking. They report that their sample contained 26 females.

a. Explain how you can set up a binary random variable X to represent gender.

b. Identify the population distribution of gender at this university. Sketch a graph.

c. Identify the data distribution of gender for this sample.

Sketch a graph.

d. Identify the sampling distribution of the sample proportion of females in the sample. State its mean and standard deviation for a random sample of size 50.

Sketch a graph.

e. Use the Sampling Distribution app accessible from the book’s website to check your answers from parts b through

d. Set the population proportion equal to p = 0.60 and n = 50. Compare the population, data, and sampling distribution graph from the app with your graphs from parts b through d.