Answer
a) .0318
b) .2676
c) Part b
d) No
Work Step by Step
a. We find:
$\mu=np=(580)(.75)=435$
$ \sigma=\sqrt{npq}=\sqrt{(580)(.25)(.75)}=10.43$
Thus, we find z:
$z=\frac{428.5-435}{10.43}=-.62$
$z=\frac{427.5-435}{10.43}=-.72$
Thus, using the table of z-scores, we find that this corresponds to a probability of $.0318$
b. We use the value of z to find:
$z=\frac{428.5-435}{10.43}=-.62$
Thus, using the table of z-scores, we find that this corresponds to a probability of $.2676$.
c) Part b) is more useful, for we want to consider the higher value.
d) No, there is not. While 26.76 percent is low, it is not low enough to prove that the study was wrong.
