Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 256.6 and a standard deviation of 69.7​(All units are 1000 ​cells/μ​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 47.5 and 465.7?

b.What is the approximate percentage of women with platelet counts between 117.2 and 396.0?

Answer 1

Empirical rule: 68 - 95 - 99.7, which indicates that 68% of data lies within 1 standard deviation from mean, 95% of data lies within 2 standard deviation from mean, and 99.7% of data lies within 3 standard deviation from mean.

a) 47.5 = 256.6 - 3*69.7

465.7 = 256.6 + 3*69.7

So, by empirical rule total 99.7% of women with platelet counts within 3 standard deviation of mean.

b) 117.2 = 256.6 - 2*69.7

396 = 256.6 + 2*69.7

So, here we see that it's asking for 2 standard deviation from mean.

Hence by empirical rule, approximately 95% of women with platelet counts between 117.2 and 396.0.

Please comment if any doubt. Thank you.