A student in a large business calculus class has a 60 chance

A student in a large business calculus class has a 60% chance of getting atleast a B. This year there was 540 students in this class. Roughly, what isthe probability that at least half of the students received at most C?

Solution

Note that

P(at most C) = 1 - P(at least B) = 1- 0.6 = 0.4.

So, p = 0.4 here.

We first get the z score for the critical value:          
          
x = critical value = 540/2 = 270      
u = mean = np =    216      
          
s = standard deviation = sqrt(np(1-p)) =    11.38419958      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    4.74341649      
          
Thus, the left tailed area is          
          
P(z >   4.74341649   ) =    1.05072*10^-6 [ANSWER]