Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 253.7 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 71.6 and 435.8​? b. What is the approximate percentage of women with platelet counts between 193.0 and 314.4​?

Answer 1

Part a)

P ( 71.6 < X < 435.8 )

Area under 71.6 < X < 435.8 will be ( 2.35 + 13.5 + 34 + 34 + 13.5 + 2.35 )% = 99.7% = 0.9970

P ( 71.6 < X < 435.8 ) = 0.9970

Part b)

P ( 193 < X < 314.4 )

Area under  193 < X < 314.4 will be ( 34 + 34 )% = 68%

P ( 193 < X < 314.4 ) = 0.6800