(Solved): please help me solve these please help me solve all the steps of the sampling diatribution of the so ...

of the sampling diatribution of the somple proportion, \( \hat{p} \). a. \( \pi=4000 \) b. \( n=1000 \) c. \( n=600 \) a. The mean is (Type an integer or a decimal Do not round.) For the binomial sample intormation summarized below, indicate whether the sample size is large enough to use the large sample approximation to construct a confísonco interval for p. \[ \mathrm{n}=50, \hat{\mathrm{p}}=0.20 \] Is the sample size large enough? A. Yes, because \( n \hat{p} \geq 15 \) and \( n \hat{q} \geq 15 \). B. No, because \( n \hat{p}<15 \) and \( \hat{n q}<15 \). c. No, because \( \hat{n} \geq 15 \) and \( \hat{n}<15 \). D. No, because \( n \hat{p}<15 \) and \( n \hat{q} \geq 15 \).