Question

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 ​?

Answer 1

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.