Answer: 0.9554
Step-by-step explanation:
Given : The proportion of the registered voters in a country are Republican = P=0.56
The number of voters = 447
The test statistic for proportion :-
[tex]z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}[/tex]
For p= 0.60
[tex]z=\dfrac{0.60-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{447}}}\approx1.70[/tex]
Now, the probability that the sample proportion of Republicans will be less than 60% (by using the standard normal distribution table):-
[tex]P(x<0.60)=P(z<1.70)=0.9554345\approx0.9554[/tex]
Hence, the probability that the sample proportion of Republicans will be less than 60% = 0.9554
