Will give Brainliest ONLY if all three parts are answered!!!!

Suppose that 20% of students at
high school A and 18% of students at high
school B
participate on a school athletic team. Independent
random samples of 30 students from each school
are selected and are asked if they participate on a
school athletic team. Let P hat A represent the sample
proportion of students at school A who participate on
a school athletic team and let P hat B represent the sample
proportion of students at school B who participate on a
school athletic team.

(a) Find the mean of the sampling distribution of P hat A - P hat B.

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

(c) Is the shape of the sampling distribution approximately
Normal? Justify your answer.