Suppose that 45 of all adult americans believe that the maj

Suppose that 45 % of all adult americans believe that the major overhaul of the nations health care delivery system is essential. What is the probability that more than 54% of a random sample of 150 adult americans would hold this belief.

The probability that more than 54% of the random sample hold this belief is

Solution

The standard deviation of the proportion is

s(p^) = sqrt(p(1-p)/n) = sqrt(0.45*(1-0.45)/150) = 0.040620192

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.54      
u = mean =    0.45      
          
s = standard deviation =    0.040620192      
          
Thus,          
          
z = (x - u) / s =    2.215646839      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.215646839   ) =    0.013357849 [ANSWER]