layer Test.aspxitestld \( =2700798798 \) centerwin \( = \) yes Alonna Harvey-Williams 2 02/05/25 12:53 PM \( \theta \) Question 11 of 82 This quiz: 82 point(s) possible This question: 1 point(s) possible Resume later Submit quiz Suppose a simple random sample of size \( n=200 \) is obtained from a population whose size is \( N=25,000 \) and whose population proportion with a specified characteristic is \( p=0.6 \). Complete parts (a) through (c) below. (a) Describe the sampling distribution of \( \hat{p} \). Choose the phrase that best describes the shape of the sampling distribution below A. Not normal because \( n \leq 0.05 \mathrm{~N} \) and \( \mathrm{np}(1-\mathrm{p})<10 \). B. Approximately normal because \( n \leq 0.05 \mathrm{~N} \) and \( n p(1-p) \geq 10 \). C. Not 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 \( \hat{p} \). \[ \stackrel{i}{\mathrm{p}}=\square \] (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of \( \hat{p} \). (1) Time Remaining: 03:18.47 Next 12:53 PM \( 2 / 5 / 2025 \) Search
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- Check if \(n \leq 0.05N\): \[ n = 200, \quad N = 25,000 \] \[ 0.05 \times 25,000 = 1,250 \] Since \(200 \leq 1,250\), the condition is satisfied. - Check if \(np(1-p) \geq 10\): \[ n = 200, \quad p = 0.6 \] \[ np(1-p) = 200 \times 0.6 Show more…
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