A simple random sample of size \( n=1000 \) is obtained from a population whose size is \( \mathrm{N}=1,500,000 \) and whose population proportion with a specified characteristic is \( p=0.33 \). (a) Describe the sampling distribution of \( \hat{p} \). Choose the phrase that best describes the shape of the sampling distribution. A. Not normal because \( n \leq 0.05 \mathrm{~N} \) and \( \mathrm{np}(1-\mathrm{p})<10 \) C. Approximately normal because \( \mathrm{n} \leq 0.05 \mathrm{~N} \) and \( \mathrm{np}(1-\mathrm{p}) \geq 10 \) D. Approximately normal because \( \mathrm{n} \leq 0.05 \mathrm{~N} \) and \( \mathrm{np}(1-\mathrm{p})<10 \) Determine the mean of the sampling distribution of \( \hat{\mathrm{p}} \). \( \mu_{\hat{p}}=\square \) (Round to two decimal places as needed.)
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