A factory employs 3000 unionized workers, 90% of whom are male. A random sample of 15 workers is selected for a survey about worker satisfaction. Let p̂ = the proportion of males in the sample.

a. Identify the mean of the sampling distribution of p̂.

b. Calculate and interpret the standard deviation of the sampling distribution of p̂. Verify that the 10% condition is met.

c. Describe the shape of the sampling distribution of p̂. Justify your answer.