In a survey 600 mothers and fathers were asked about the imp

In a survey, 600 mothers and fathers were asked about the importance of sports for boys and girls. Of the parents interviewed, 70% said the genders are equal and should have equal opportunities to participate in sports. A. What are the mean, standard deviation, and shape of the distribution of the sample proportion p-hat of parents who say the genders are equal and should have equal opportunities?

*I am struggling on how to know the distribution. Is it approx. normal because of the central limit theorem? Or is it rightly skewed?

Solution

Here,          

n =    600      
p =    0.7      

Thus, the mean and standard deviation are

u = mean = p =    0.7   [ANSWER]  
          
s = standard deviation = sqrt(p(1-p)/n) =    0.018708287   [ANSWER]

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It is approximately normal because np and n(1-p) are both greater than 10.