Sale Price of Homes The average sale price of new one-family houses in the United States for a recent year was \( \$ 242,900 \) Find the range of values in which at least \( 75 \% \) of the sale prices will lie if the standard deviation is \( \$ 47,500 \). Round your \( k \) to the nearest whole number. The range of values is between \( \$ \square \) and \( \$ \square \)

To find the range of values in which at least 75% of the sale prices will lie, we can use the empirical rule (68-95-99.7 rule). Since 75% isn't directly covered by the empirical rule, we can use the z-score corresponding to 75% of the data, which is approximately \( z = 1.15 \) (you may also use z-tables for more precise values). Now, we calculate the range: - Lower limit: \( 242,900 - (1.15 \times 47,500) \) - Upper limit: \( 242,900 + (1.15 \times 47,500) \) Calculating that gives: - Lower limit: \( 242,900 - 54,625 = 188,275 \) - Upper limit: \( 242,900 + 54,625 = 297,525 \) So, the range of values where at least 75% of the sale prices will lie is between \( \$ 188,275 \) and \( \$ 297,525 \). Happy house-hunting!