Of all 3 to 5year old children 56 are enrolled in school If

Of all 3- to 5-year old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, find the probability that at least 251 will be enrolled in school. Round the final answer to 4 decimal places and round intermediate z-value calculations to 2 decimal places. Source: Statistical Abstract of the United States. P(X GE 251) =

Solution

As

mean = np = 500*0.56 = 280

standard deviation = sqrt(np(1-p)) = sqrt(500*0.56*(1-0.56)) = 11.09954954

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    250.5      
u = mean =    280      
          
s = standard deviation =    11.09954954      
          
Thus,          
          
z = (x - u) / s =    -2.66      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -2.66   ) =    0.996092967 [ANSWER]