Suppose 56% of the registered voters in a country are Republican. If a sample of 447 voters is selected, what is the probability that the sample proportion of Republicans will be less than 60%? Round your answer to four decimal places.
Accepted Solution
A:
Answer: 0.9554Step-by-step explanation:Given : The proportion of the registered voters in a country are Republican = P=0.56The number of voters = 447The 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