Answer
a) $0.002$
b) Yes, it is.
c) Yes
Work Step by Step
a. We find:
$μ=np=(1004)(0.25)=251$
$σ=\sqrt{npq}=\sqrt{(1004)(0.25)(0.75)}=13.72$
Hence, we find z:
$z=\frac{290.5−251}{13.72}=2.88$
Thus, using the table of z-scores, we can find that the corresponding probability is: $1−0.9980=0.002$.
b) It is unusually high, because the odds of getting this high is only $0.2$ percent if the rate is correct.
c) Assuming this study was correct, the data suggest that the percentage is actually more than $25$ percent, because the odds of getting $291$ if the actual percentage is $25$ percent is only $0.2$ percent.
