help -probablity problem


New Member
Hello every one , i just registered to this forum .Currently i am studying stats , Can you please help me on how to solve bellow problem :

"Approximately 85% of statistics students do their homework in time for it to be collected and graded. Let X be the number students that submit their homework in time out of a statistics class of 70 students. The following 4 questions refer to this X. (The answer may be rounded up to 3 decimal places of the actual value.) "

How i can find the following :

Which type of random distribution there?

The probability that less than 60 of the 70 students will do their homework on time is?

The expectation of X is:?

Thanks in advance .


TS Contributor
Assume that all 70 students are independent, and they have the same
probability \( p = 85\% \) to do their homework in time.

Now \( X \) is counting the total number of students to do their
homework in time in the class.

Then \( X \sim Binomial (70, 85\%) \)

When you are counting the sum of \( n \) independent and identically
distributed \( Bernoulli(p) \) trials,
you have the \( Binomial(n, p) \) distribution

The rest of the problem is easy once you can figure out the distribution.
You can go to study the Binomial distribution if you are not familiar with that.