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.
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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