Question

The biood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.7 and a standard deviation of 61.7. (All units are 1000 cells/uL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 68.6 and 438.8 ?

Answer 1

The empirical rule, also known as the 68-95-99.7 rule, provides approximate percentages of data within specific standard deviation ranges for a bell-shaped (normal) distribution. Here's how you can find the approximate percentage of women with platelet counts within 3 standard deviations of the mean:

1. Calculate the lower and upper bounds for the range within 3 standard deviations of the mean:

Lower Bound = Mean - (3 * Standard Deviation)

Upper Bound = Mean + (3 * Standard Deviation)

Lower Bound = 253.7 - (3 * 61.7) = 253.7 - 185.1 = 68.6

Upper Bound = 253.7 + (3 * 61.7) = 253.7 + 185.1 = 438.8

So, the platelet counts within 3 standard deviations of the mean are between 68.6 and 438.8.

2. To find the approximate percentage within this range using the empirical rule:

- Approximately 99.7% of the data falls within 3 standard deviations of the mean.

So, the approximate percentage of women with platelet counts between 68.6 and 438.8 is approximately 99.7%.

Explanation: