Question

The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 254.7 and a standard deviation of 67.6. (All units are 1000 cells/ L.) 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 51.9 and 457.5?

b. What is the approximate percentage of women with platelet counts between 187.1 and 322.3?

Answer 1

Using the Empirical Rule, more than 99% of the women have platelet counts within 3 standard deviations of the mean (51.9 to 457.5), and approximately 68% have counts between one standard deviation from the mean (187.1 to 322.3).

Step-by-step explanation:

According to the Empirical Rule for bell-shaped distributions:

• Approximately 68% of the data lies within one standard deviation of the mean.
• Approximately 95% of the data lies within two standard deviations of the mean.
• More than 99% of the data lies within three standard deviations of the mean.

a. To find the approximate percentage of women with platelet counts within 3 standard deviations of the mean, we would use the Empirical Rule that states more than 99% of the data falls within this range. Thus, the approximate percentage is more than 99%.

b. The percentage of women with platelet counts between 187.1 (254.7 - 67.6) and 322.3 (254.7 + 67.6), which is within one standard deviation of the mean, is approximately 68% as per the Empirical Rule.