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Answer :
Final answer:
The empirical rule states that for data with a bell-shaped distribution, a certain percentage of the data falls within a certain number of standard deviations from the mean. Using this rule, we can find the percentage of women with platelet counts within a given range. For part a, the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.9 and 441.5, is greater than 99%. For part b, we can calculate the z-scores for the given platelet count range and use them to find the corresponding percentage.
Explanation:
The empirical rule states that for data with a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and more than 99% falls within three standard deviations.
For part a, the platelet counts between 65.9 and 441.5 are within 3 standard deviations of the mean. Using the empirical rule, approximately 99% (more than 99%) of women have platelet counts within 3 standard deviations of the mean.
For part b, to find the percentage of women with platelet counts between 128.5 and 378.9, we need to calculate the z-scores for these values:
Z-score for 128.5: (128.5 - 253.7) / 62.6 = -2. milliseconds
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