Answer
a) $0$ percent
b) Unusually high
c) Part b)
d) Yes
Work Step by Step
a. We find:
$μ=np=(945)(0.5)=472.5$
$σ=\sqrt{npq}=\sqrt{(945)(0.5)(0.5)}=15.37$
Hence, we find z:
$z=\frac{878.5−472.5}{15.37}=26.41 $
$z=\frac{879.5−472.5}{15.37}=26.47 $
Thus, using the table of z-scores, we can find that the corresponding probability is: $0.0000$.
b) We find z:
$z=\frac{878.5−472.5}{15.37}=26.41$
Thus, using the table of z-scores, we can find that the corresponding probability is $0.0001$. Since the probability is so small that it is nearly $0$ percent, this number is unusually high.
c) Part b) is more useful, because we do not care about getting exactly $845$ girls, rather, we care whether or not $845$ or more is a large number.
d) Yes, it is, because the odds of getting this high of a number by chance is almost $0$.
