Question 1175474
Assuming randomness etc.
test stat is a z=(p hat-p)/sqrt(p*(1-p)/n)
Critical value is z< -2.33
=-.07/sqrt(.9*.1/500)
=.-.07/0.013
=-5.21
reject Ho
p-value <0.0001 (4 x 10^(-7)
Note: realistically have to use 416 or 417 for the numerator of the proportion since 83% of 500 is not an integer. It doesn't change the answer.

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Probability is 0.2490 that it is >0.61. (0.7510 that it is 239 or fewer)
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check with the normal approximation, which ought to be about this.

np=mean or 233.02
np(1-p)=variance or 90.8778 
sd is sqrt(V)=9.53
z>(239.5-233.02/9.53  which is 6.48/9.53 or z > 0.68 which is prob. 0.2482
Use the answer above of 0.2490.