Given that X is a Binomial RV with mean 60 and standard devi

Given that X is a Binomial RV with mean 60 and standard deviation 5, approximate the probability that X is at most 68

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    68.5      
u = mean =    60      
          
s = standard deviation =    5      
          
Thus,          
          
z = (x - u) / s =    1.7      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.7   ) =    0.044565463 [ANSWER]