## Elementary Statistics (12th Edition)

a) $0.002$ b) Yes, it is. c) Yes
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.