1. **State the problem:** We are given a mean platelet count of $255.1$ and a standard deviation of $65.2$. We want to use Chebyshev's theorem to find the minimum percentage of women with platelet counts within 3 standard deviations of the mean, and also find the minimum and maximum platelet counts within this range. 2. **Chebyshev's theorem formula:** For any distribution, the proportion of data within $k$ standard deviations of the mean is at least $$1 - \frac{1}{k^2}$$ where $k > 1$. 3. **Calculate the minimum percentage within 3 standard deviations:** $$1 - \frac{1}{3^2} = 1 - \frac{1}{9} = \frac{8}{9} \approx 0.8889$$ Multiply by 100 to get percentage: $$0.8889 \times 100 = 88.89\%$$ Rounded to the nearest integer, this is $89\%$. 4. **Calculate the minimum and maximum platelet counts within 3 standard deviations:** Minimum count: $$255.1 - 3 \times 65.2 = 255.1 - 195.6 = 59.5$$ Maximum count: $$255.1 + 3 \times 65.2 = 255.1 + 195.6 = 450.7$$ **Final answers:** - At least $89\%$ of women have platelet counts within 3 standard deviations of the mean. - The minimum possible platelet count within 3 standard deviations is $59.5$. - The maximum possible platelet count within 3 standard deviations is $450.7$.