Of the 13,500 savings accounts in a bank, 4,675 belong to people younger than 40 years old. The bank president would lik to increase her institution's marketing strategy to younger customers, so she is examining the population proportions in order to create a statistical study.

Find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size $n=400$.

Round all answers to 3 decimal places.

Provide your answer below:
\[
\begin{array}{l}
p=\square \\
\mu_{p}=\square \\
\sigma_{p}=\square
\end{array}
\]

Step 1 ：First, we need to calculate the population proportion (p). This can be done by dividing the number of accounts belonging to people younger than 40 (4675) by the total number of accounts (13500).

Step 2 ：Next, we calculate the mean of the sampling distribution (μp), which is equal to the population proportion (p).

Step 3 ：Finally, we calculate the standard deviation of the sampling distribution (σp) using the formula \(\sqrt{p(1-p)/n}\), where n is the sample size (400).

Step 4 ：Let's calculate these values.

Step 5 ：The population proportion (p) is \( \frac{4675}{13500} = 0.346 \).

Step 6 ：The mean of the sampling distribution (μp) is equal to the population proportion (p), so \( \mu_{p} = 0.346 \).

Step 7 ：The standard deviation of the sampling distribution (σp) is calculated as \( \sqrt{\frac{0.346(1-0.346)}{400}} = 0.024 \).

Step 8 ：So, the final answer is: \(\boxed{p=0.346}\), \(\boxed{\mu_{p}=0.346}\), \(\boxed{\sigma_{p}=0.024}\).