Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean...

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 256.4 and a standard deviation of 60.8. ​(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 1 standard deviation of the​ mean, or between 195.6 and 317.2​? b. What is the approximate percentage of women with platelet counts between 74.0 and 438.8​? a. Approximately what​% of women in this group have platelet counts within 1 standard deviation of the​ mean, or between 195.6 and 317.2.

Solution :

Given that,

mean = = 256.4

standard deviation = = 60.8

Using Empirical rule,

a) P( - < x <   + ) = 68%

= P( 256.4 - 60.8 < x < 256.4 + 60.8 ) = 68%

= P( 195.6 < x < 317.2 ) =68%

b) P( - 3 < x <   + 3 ) = 99.7%

= P( 256.4 - 3 * 60.8 < x < 256.4 + 3 * 60.8 ) = 99.7%

= P( 256.4 - 182.4 < x < 256.4 + 182.4 ) = 99.7%

=P( 74.0 < x < 438.8 ) = 99.7%