Question

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of

264.6264.6

and a standard deviation of

62.562.5.

​(All units are 1000

​cells/muμ​L.)

Using the empirical​ rule, find each approximate percentage below.

a.	What is the approximate percentage of women with platelet counts within 33 standard deviationsdeviations of the​ mean, or between 77.177.1 and 452.1452.1​?
b.	What is the approximate percentage of women with platelet counts between 139.6139.6 and 389.6389.6​?

a. Approximately

nothing​%

of women in this group have platelet counts within

33

standard

deviationsdeviations

of the​ mean, or between

77.177.1

and

452.1452.1.

Answer 1

Given $\mu = 264.6$ and $\sigma =77.1$

a) $Z_{1} =\frac{X_{1}-\mu }{\sigma }=\frac{77.1-264.6}{62.5}=\frac{-187.5}{62.5}=-3$

$Z_{2 }=\frac{X_{2}-\mu }{\sigma }=\frac{452.1-264.6}{62.5}=\frac{187.5}{62.5}=3$

b) $Z_{1} =\frac{X_{1}-\mu }{\sigma }=\frac{139.6-264.6}{62.5}=\frac{-125}{62.5}=-2$

$Z_{2} =\frac{X_{2}-\mu }{\sigma }=\frac{389.6-264.6}{62.5}=\frac{125}{62.5}=2$