The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 261.3 and a standard deviation of 64.2. (All units are 1000 cells/ μL.) 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 68.7 and 453.9? b. What is the approximate percentage of women with platelet counts between 197.1 and 325.5?
mean = 261.3
sd = 64.2
As per Empirircal rule:
Approx. 68% of the data lies between ± 1 SD, or between 197.10 and 325.5
Approx. 95% of the data lies between ± 2 SD, or between 132.9 and 389.70
Approx. 99.7% of the data lies between ± 3 SD, or between 68.70
and 453.90
a) percentage of women with platelet counts within 3 standard
deviations of the mean, or between 68.7 and 453.9
ANS: Approx. 99.7% of the data lies between mean ± 3 SD, or between 68.70 and 453.90
b) Approximate percentage of women with platelet counts between 197.1 and 325.5
ANS: Approx. 68% of the data lies between mean ± 1 SD, or between 197.10 and 325.5
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