Question

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/muL.) 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.

Answer #1

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%

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