Answer: A. 5%
Step-by-step explanation:
Given : The chance that they will join the graduate program : p=0.10
The total number of students in the class: n = 400
For this binomial situation :

We assume that this is normal distribution.
Let X be the random variable that represents the students will be joining a graduate program.
Z-score : 
For x= 50 , we have

Using the standard normal distribution table , we have

Hence, the value i.e.closest to the probability that at least 50 students will be joining a graduate program = 5%
Okay, this is a written proof so what you have to do is list the steps. I am going to try my best to solve this problem...
The first thing to do is to clear the equation of fractions by multiplying by its LCM, which is 6 in this case. When you do that, you will get the equation
4p + 36 = 7p. Much easier to deal with, right? Now move the 4p over by subrtracting it: 36 = 3p, and p = 12