# help -probablity problem

#### newp

##### 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:?

#### BGM

##### 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.