Question 1168212
Let $X$ be the random variable representing the price of a new one-family home. We are given that $X$ follows a normal distribution with a mean ($\mu$) of $246,300 and a standard deviation ($\sigma$) of $15,000.

We want to find the minimum and maximum prices that satisfy the middle 88% of the market. This means that the area in the tails is $100\% - 88\% = 12\%$, with $6\%$ in each tail. We need to find the z-scores that correspond to the 6th percentile and the 94th percentile of the standard normal distribution.

Looking up the z-value for a cumulative probability of $0.06$ in a standard normal distribution table, we get approximately $z_1 = -1.55$.
Looking up the z-value for a cumulative probability of $0.94$ in a standard normal distribution table, we get approximately $z_2 = 1.55$.

Now, we use the z-score formula to convert these z-values back to the original price scale:
$z = \frac{x - \mu}{\sigma}$

For the minimum price ($x_{min}$), using $z_1 = -1.55$:
$-1.55 = \frac{x_{min} - 246,300}{15,000}$
$x_{min} - 246,300 = -1.55 \times 15,000$
$x_{min} - 246,300 = -23,250$
$x_{min} = 246,300 - 23,250$
$x_{min} = 223,050$

Rounding to the nearest dollar, the minimum price is $223,050$.

For the maximum price ($x_{max}$), using $z_2 = 1.55$:
$1.55 = \frac{x_{max} - 246,300}{15,000}$
$x_{max} - 246,300 = 1.55 \times 15,000$
$x_{max} - 246,300 = 23,250$
$x_{max} = 246,300 + 23,250$
$x_{max} = 269,550$

Rounding to the nearest dollar, the maximum price is $269,550$.

Final Answer: The final answer is $\boxed{Minimum Price: 223050, Maximum Price: 269550}$