Part 5 of 8 Points: 0.38 of 1 According to a survey in a country, $28 \%$ of adults do not own a credit card. Suppose a simple random sample of 900 adults is obtained. Complete parts (a) through (d) below. C. Approximately normal because $n \leq 0.05 \mathrm{~N}$ and $n p(1-p)<10$ D. Not normal because $n \leq 0.05 \mathrm{~N}$ and $n p(1-p) \geq 10$ Determine the mean of the sampling distribution of $\hat{p}$. $\mu_{p}=0.28$ (Round to two decimal places as needed.) Determine the standard deviation of the sampling distribution of $\hat{p}$. $\sigma_{p}=0.015$ (Round to three decimal places as needed.) (b) What is the probability that in a random sample of 900 adults, more than $31 \%$ do not owh a credit card? The probability is 0.0225 . (Round to four decimal places as needed.) Interpret this probability. If 100 different random samples of 900 adults were obtained, one would expect $\square$ to result in more than $31 \%$ not owning a credit card. (Round to the nearest integer as needed.)

Step 1 ：According to a survey in a country, 28% of adults do not own a credit card. Suppose a simple random sample of 900 adults is obtained.

Step 2 ：The mean of the sampling distribution of \(\hat{p}\) is \(\mu_{p}=0.28\).

Step 3 ：The standard deviation of the sampling distribution of \(\hat{p}\) is \(\sigma_{p}=0.015\).

Step 4 ：The probability that in a random sample of 900 adults, more than 31% do not own a credit card is 0.0225.

Step 5 ：If 100 different random samples of 900 adults were obtained, we would expect to calculate the number of samples that result in more than 31% not owning a credit card by multiplying the total number of samples (100) by the probability (0.0225).

Step 6 ：\(\text{total_samples} = 100\)

Step 7 ：\(\text{probability} = 0.0225\)

Step 8 ：\(\text{expected_samples} = \text{total_samples} \times \text{probability} = 2.25\)

Step 9 ：Rounding \(\text{expected_samples}\) to the nearest integer gives 2.

Step 10 ：Final Answer: If 100 different random samples of 900 adults were obtained, one would expect \(\boxed{2}\) to result in more than 31% not owning a credit card.