The problem says that the probability of student failure is 0.4 A random sample of size 10 is taken from this population. I'm asked to find the probability that, at most, 30 % of students failed.
I don't understand how to start but I'll try:
sample size $n = 10$, then the degrees of freedom $ \nu = n -1 = 9$, if the probability of one student failing is $0.4$, then the expected value of the sample $ \bar x = (0.4) (10) = 4$?
I'm not sure about that last part, now to find the probability of at most 30 % students failed, should I calculate:
$ P( T <0.3)$ ? I'm really lost, I only understand the difference between the t-distribution and the normal distribution, but don't understand how to solve these kinds of problems or how to make sense out of them, hopefully you can help me, thanks.