**QUESTION**

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2. 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 $\hat{p}_{S}-\hat{p}_{j}$ be the difference in the sample proportions of seniors and juniors that have parking passes. a. What is the shape of the sampling distribution of $\hat{p}_{S}-\hat{p}_{\text {}}$ ? 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 $30 \%$ ?

2. 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 $\hat{p}_{S}-\hat{p}_{j}$ be the difference in the sample proportions of seniors and juniors that have parking passes. a. What is the shape of the sampling distribution of $\hat{p}_{S}-\hat{p}_{\text {}}$ ? 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 $30 \%$ ?

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