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 62.6. ​(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 2 standard deviations of the​ mean, or between 129.4 and 379.8​?

b. What is the approximate percentage of women with platelet counts between 192.0 and 317.2​?

Answer 1

Solution :

Given that,

mean = = 254.6

standard deviation = = 62.6

Using Empirical rule,

a) P( - 2 < x <   + 2 ) = 95%

= P( 254.6 - 2 * 62.6 < x < 254.6 + 2 * 62.6 ) = 95%

=P( 129.4 < x < 379.8 ) = 95%

Approximately = 95%

b) P( - < x <   + ) = 68%

= P( 254.6 - 62.6 < x < 254.6 + 62.6 ) = 68%

= P( 192.0 < x < 317.2 ) =68%

Approximately = 68%