Probability help?

Question

In a random poll of MDM4UE students , it was determined that 90% of students submitted tests before ultimate deadline. In a random sample of 75, what is the probability that exactly 10 submitted after the ultimate deadline? We are assuming all students submit. What is the probability that less than 10 submitted after the deadline?

Answer 1

Let N be the number of students in the sample submitting after the deadline.

 

The true probability is based on the binomial distribution Bin(n=75 , p=0.1). Here we assume every student's submission is independent.

 

Thus P(N=10) = C(75,10) · 0.1¹⁰ · 0.9⁶⁵ = 0.087959...

 

Or about 8.8% chance.