At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects a SRS of 30 seniors and a separate SRS of 30 juniors. Let ^ps-^pj be the difference in the sample proportic seniors and juniors that have parking passes.
a. What is the shape of the sampling distribution of ^ps-^pj? Why?
b. Find the mean of the sampling distribution.
c. Calculate and interpret the standard deviation of the sampling distribution.
d. What is the probability that the difference in sample proportions (senior-junior) of students with parking passes is greater than 30%?