Work e blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.8 and a standard deviation of 63.3 . (All units are 1000 cells/uL.) Using II pirical rule, find each approximate percentage below. \( 61,11 \%, 3.67 \) of 6 points a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 127.2 and 380.4 ? b. What is the approximate percentage of women with platelet counts between 63.9 and 443.7 ? 1

To determine the approximate percentages of women with platelet counts within specific ranges using the **Empirical (68-95-99.7) Rule**, we proceed as follows: ### Given: - **Mean (μ)** = 253.8 (in 1000 cells/uL) - **Standard Deviation (σ)** = 63.3 (in 1000 cells/uL) ### Empirical Rule Overview: - **Within 1 standard deviation (μ ± σ):** ~68% - **Within 2 standard deviations (μ ± 2σ):** ~95% - **Within 3 standard deviations (μ ± 3σ):** ~99.7% ### a. Platelet Counts Within 2 Standard Deviations (127.2 to 380.4) **Calculation:** - Lower Bound: μ - 2σ = 253.8 - (2 × 63.3) = 253.8 - 126.6 = **127.2** - Upper Bound: μ + 2σ = 253.8 + (2 × 63.3) = 253.8 + 126.6 = **380.4** **Approximate Percentage:** - According to the Empirical Rule, ~**95%** of the data falls within 2 standard deviations of the mean. ### b. Platelet Counts Between 63.9 and 443.7 **Calculation:** - Lower Bound: μ - 3σ = 253.8 - (3 × 63.3) = 253.8 - 189.9 = **63.9** - Upper Bound: μ + 3σ = 253.8 + (3 × 63.3) = 253.8 + 189.9 = **443.7** **Approximate Percentage:** - According to the Empirical Rule, ~**99.7%** of the data falls within 3 standard deviations of the mean. ### **Summary:** - **a.** Approximately **95%** of women have platelet counts between **127.2** and **380.4** (within 2 standard deviations). - **b.** Approximately **99.7%** of women have platelet counts between **63.9** and **443.7** (within 3 standard deviations).