At a university, 55% of the 6500 students are female.

The student newspaper reports results of a survey of a random sample of 60 students about the activity clubs they wish to join. They report that their sample contained 32 females.

(a) Explain how you can set up a variable y to represent gender.

(b) Identify the population distribution of gender at this university.

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

(d) The sampling distribution of the sample proportion of females in the sample is approximately a normal distribution with mean 0.55 and standard error 0.07.

Explain what this means.