Question

Suppose that 42\%42%42, percent of students of a high school play video games at least once a month. The computer programming club takes an SRS of 303030 students from the population of 792792792 students at the school and finds that 40\%40%40, percent of students sampled play video games at least once a month. The club plans to take more samples like this. Let \hat p p ^ ​ p, with, hat, on top represent the proportion of a sample of 303030 students who play video games at least once a month. What are the mean and standard deviation of the sampling distribution of \hat p p ^ ​ p, with, hat, on top? Choose 1 answer: Choose 1 answer: (Choice A) A \begin{aligned} \mu_{\hat p}&=0.42 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.42\left(0.58\right)}{30}} \end{aligned} μ p ^ ​ ​ σ p ^ ​ ​ ​ =0.42 = 30 0.42(0.58) ​ ​ ​ (Choice B) B \begin{aligned} \mu_{\hat p}&=(30)(0.42) \\\\ \sigma_{\hat p}&=\sqrt{30(0.42)(0.58)} \end{aligned} μ p ^ ​ ​ σ p ^ ​ ​ ​ =(30)(0.42) = 30(0.42)(0.58) ​ ​ (Choice C) C \begin{aligned} \mu_{\hat p}&=(30)(0.4) \\\\ \sigma_{\hat p}&=\sqrt{30(0.4)(0.6)} \end{aligned} μ p ^ ​ ​ σ p ^ ​ ​ ​ =(30)(0.4) = 30(0.4)(0.6) ​ ​ (Choice D) D \begin{aligned} \mu_{\hat p}&=0.4 \\\\ \sigma_{\hat p}&=\sqrt{\dfrac{0.4\left(0.6\right)}{30}} \end{aligned} μ p ^ ​ ​ σ p ^ ​ ​ ​ =0.4 = 30 0.4(0.6) ​ ​ ​

Answer 1

Answer:

its A, first choice on khan

Explanation: