Answer
a) .002
b) Yes, it is.
c) Yes
Work Step by Step
a. We find:
$\mu=np=(1004)(.25)=251$
$ \sigma=\sqrt{npq}=\sqrt{(1004)(.25)(.75)}=13.72$
Thus, we find z:
$z=\frac{290.5-251}{13.72}=2.88$
Thus, using the table of z-scores, we find that this corresponds to a probability of $1-.9980=.002$
b) It is unusually high, for the odds of getting this high is only .2 percent if the rate is correct.
c) Assuming this study was correct, the data suggest that the percentage is actually above 25 percent, for the odds of getting 291 if the actual percentage is 25 percent is only .2 percent.
