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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. 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

In a bell-shaped distribution, also known as a normal distribution, the empirical rule provides a handy framework to understand how data is spread. According to this rule, about 68% of the data falls within one standard deviation of the mean, roughly 95% within two standard deviations, and about 99.7% within three standard deviations. So, for your first question, about 95% of women would have platelet counts between 127.2 and 380.4, as this range covers two standard deviations from the mean.

Now, for the second part, we need to look beyond two standard deviations. The range you provided, from 63.9 to 443.7, encompasses well beyond two standard deviations on either side. This means you’re likely capturing nearly all of the dataset. In fact, since this range extends into the three standard deviations (approximately 99.7% of the population), we can estimate that close to 99.7% of women will have platelet counts lying within this range. So, you’re really looking at almost everyone in this group!