Question

The blood platelet counts of a group of women have a​bell-shaped distribution with a mean of 254.6 and a standard deviation of 60.7. ​(All units are 1000 ​cells/mu​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 72.5 and 436.7​? b. What is the approximate percentage of women with platelet counts between 133.2 and 376.0​?

Answer 1

a) According to empirical rule of bell shaped distribution, about 99.7% of the observations lies within 3 standard deviations of the mean. Therefore 99.7% of the observations lies between 72.5 and 436.7

b) 133.2 = 254.6 - 2*60.7 that is 2 standard deviations less than the mean.
376 = 254.6 + 2*60.7 that is 2 standard deviations more than the mean.

According to empirical rule, 95% of the observations lies within 2 standard deviations of the mean. Therefore 95% is the required answer here.