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.)
Answer
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.
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.
