Suppose that 35% of students in a school can sing their national anthem correctly. The music teacher takes an SRS of 30 students from the population of 750 students at the school and finds that 40% of students sampled can sing their national anthem correctly. The teacher plans to take more samples like this.
Let ^p represent the proportion of a sample of 30 students in the school who can sing their national anthem correctly.
What are the mean and standard deviation of the sampling distribution of ^p?