Answer
a) $0.0318$
b) $0.2676$
c) Part )
d) No
Work Step by Step
a. We find:
$μ=np=(580)(0.75)=435$
$σ=\sqrt{npq}=\sqrt{(580)(0.25)(0.75)}=10.43$
Hence, we find z:
$z=\frac{428.5−435}{10.43}=−0.62 $
$z=\frac{427.5−435}{10.43}=−0.72 $
Thus, using the table of z-scores, we can find that the corresponding probability is: $0.0318 $.
b) We find z:
$z=\frac{428.5−435}{10.43}=−0.62 $
Thus, using the table of z-scores, we can find that the corresponding probability is $0.2676$.
c) Part b) is more useful, because we want to consider the higher value.
d) No, there is not. Although $26.76$ percent is low, it is not low enough to prove that the study was wrong.