Questions: According to a survey in a country, 32% of adults do not own a credit card. Suppose a simple random sample of 400 adults is obtained. Complete parts (a) through (d) below. (a) Describe the sampling distribution of p̂, the sample proportion of adults who do not own a credit card. Choose the phrose that best describes the shape of the sampling distribution of pbelow. A. Not normal because n ≤ 0.05 N and np(1-p)<10 B. Not normal because n ≤ 0.05 N and np(1-p) ≥ 10 C. Approximately normal because n ≤ 0.05 N and np(1-p)<10 D. Approximately normal because n ≤ 0.05 N and np(1-p) ≥ 10 Determine the mean of the sampling distribution of p̂. μp= (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of p̂. σp̂= (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 400 adults, more than 34% do not own a credit card? The probability is (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 400 adults were obtained, one would expect to result in more than 34% not owning a credit card. (Round to the nearest integer as needed.)

Transcript text: According to a survey in a country, $32 \%$ of adults do not own a credit card. Suppose a simple random sample of 400 adults is obtained. Complete parts (a) through (d) below. (a) Describe the sampling distribution of $\hat{p}$, the sample proportion of adults who do not own a credit card. Choose the phrose that best describes the shape of the sampling distribution of pbelow. A. Not normal because $n \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p})<10$ B. Not normal because $\mathrm{n} \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p}) \geq 10$ C. Approximately normal because $n \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p})<10$ D. Approximately normal because $\mathrm{n} \leq 0.05 \mathrm{~N}$ and $\mathrm{np}(1-\mathrm{p}) \geq 10$ Determine the mean of the sampling distribution of $\hat{p}$. $\mu_{\mathrm{p}}=\square$ $\square$ (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of $\hat{p}$. $\sigma_{\hat{p}}=\square$ $\square$ (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 400 adults, more than $34 \%$ do not own a credit card? The probabaity is $\square$ (Round to four decimal places as needed.) Interpet this probability. If 100 different random samples of 400 adults were obtained, one would expect $\square$ to result in more than $34 \%$ not owning a credit card. (Round to the nearest integer as needed.)