The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 261.5 and a standard deviation of 67.4 . (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 194.1 and 328.9 ? b. What is the approximate percentage of women with platelet counts between 59.3 and 463.7 ?

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Answer 1

Answer: To solve this problem using the empirical rule, we will use the following percentages:

- Approximately 68% of the data falls within 1 standard deviation of the mean.
- Approximately 95% of the data falls within 2 standard deviations of the mean.
- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

a. To find the approximate percentage of women with platelet counts within 1 standard deviation of the mean, we can use the 68% rule. Since 194.1 is 1 standard deviation below the mean, and 328.9 is 1 standard deviation above the mean, we can say that approximately 68% of the women have platelet counts within this range.

b. To find the approximate percentage of women with platelet counts between 59.3 and 463.7, we can use the 95% rule. Since 59.3 is 2 standard deviations below the mean, and 463.7 is 2 standard deviations above the mean, we can say that approximately 95% of the women have platelet counts within this range.

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Terminal point definition the final destination or station of a bus or rail journey | Meaning, pronunciation, translations, and examples.

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