Using GC to find range of values of p in Binomial Distribution

A course takes in exactly 10 students. On average, a student has p% chance of achieving a distinction.

Given that the probability 7 students scoring distinction is greater than the probability of any other number of students scoring distinction, find the possible range of values of p.

Solution

Since the question did not ask for exact values of p, we can use the GC to solve this question.

We are looking at where the blue graph is above the red and black graph.

Hence 63.6<p<72.7