the proportion of students at a large high school who live within five miles of the school is $p = 0.19$…

the proportion of students at a large high school who live within five miles of the school is $p = 0.19$. the principal takes a random sample of 17 students from this school. which is the best description of the shape for the sampling distribution of $hat{p}$?\nthe sampling distribution of $hat{p}$ is approximately normal because $n(1 - p)=13.77>10$.\nbecause $np = 17(0.19)=3.23<10$, the sampling distribution of $hat{p}$ is not approximately normal. the sampling distribution of $hat{p}$ is skewed left and centered at 0.81.\nbecause $np = 17(0.19)=3.23<10$, the sampling distribution of $hat{p}$ is not approximately normal. because $p = 0.19$ is closer to 0 than 1, the sampling distribution of $hat{p}$ is skewed to the left.\nbecause $np = 17(0.19)=3.23<10$, the sampling distribution of $hat{p}$ is not approximately normal. because $p = 0.19$ is closer to 0 than 1, the sampling distribution of $hat{p}$ is skewed to the right.

the proportion of students at a large high school who live within five miles of the school is $p = 0.19$. the principal takes a random sample of 17 students from this school. which is the best description of the shape for the sampling distribution of $hat{p}$?\nthe sampling distribution of $hat{p}$ is approximately normal because $n(1 - p)=13.77>10$.\nbecause $np = 17(0.19)=3.23<10$, the sampling distribution of $hat{p}$ is not approximately normal. the sampling distribution of $hat{p}$ is skewed left and centered at 0.81.\nbecause $np = 17(0.19)=3.23<10$, the sampling distribution of $hat{p}$ is not approximately normal. because $p = 0.19$ is closer to 0 than 1, the sampling distribution of $hat{p}$ is skewed to the left.\nbecause $np = 17(0.19)=3.23<10$, the sampling distribution of $hat{p}$ is not approximately normal. because $p = 0.19$ is closer to 0 than 1, the sampling distribution of $hat{p}$ is skewed to the right.

Answer

Answer:

Because $np = 17(0.19)=3.23<10$, the sampling distribution of $\hat{p}$ is not approximately Normal. Because $p = 0.19$ is closer to $0$ than $1$, the sampling distribution of $\hat{p}$ is skewed to the left.

Explanation:

Step1: Check normal - approximation condition

We use the rule that for the sampling distribution of $\hat{p}$ to be approximately normal, $np\geq10$ and $n(1 - p)\geq10$. Here, $n = 17$ and $p=0.19$. Calculate $np=17\times0.19 = 3.23<10$ and $n(1 - p)=17\times(1 - 0.19)=17\times0.81 = 13.77>10$. Since $np<10$, the sampling distribution is not approximately normal.

Step2: Determine the skew

When $p$ is close to $0$, the sampling distribution of $\hat{p}$ is skewed to the left. Since $p = 0.19$ is close to $0$, the sampling distribution of $\hat{p}$ is skewed to the left.