Answer
a. .9787
b. 21.08 to 24.22
c. .9998; No
Work Step by Step
a) We first find the two z-scores:
$z=\frac{25-22.65}{.8}=2.94$
$z=\frac{21-22.65}{.8}=-2.06$
Using the table of z-scores, we find:
$=.9984-.0197=.9787$
b) Using the table of negative z-scores, we find that this corresponds to a value of z of $\pm1.96$. Thus, it follows:
$max=22.65+(.8)(1.96)=24.22$
$min=22.65+(.8)(-1.96)=21.08$
c) Using z-scores, we find that the probability is .9998. However, since this represents the mean of women and not the general population, it does not follow that the majority of women will be able to fit in these hats.
