Question

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?

Answer #1

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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