According to the regional bar association aproximately 60 of

According to the regional bar association, aproximately 60% of the people that take the bar exam to practice law in the region pass the exam. Find the aproximate probability that atleast 62% of 300 randomly sampled people taking the bar exam will pass.

Using the normal approximation, what is the probability that atleast 62% of 300 randomly sampled people takind the bar exam will pass.

Round to three decimal places as needed

Solution

Here, the standard deviation of proportions is

s(p^) = sqrt(p(1-p)/n) = sqrt(0.60*(1-0.60)/300) = 0.028284271

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    0.62      
u = mean =    0.6      
          
s = standard deviation =    0.028284271      
          
Thus,          
          
z = (x - u) / s =    0.707106787      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0.707106787   ) =    0.239750059 [ANSWER]