Using the binomial distribution, it is found that there is a 0.2617 = 26.17% probability that at least 8 but at most 10 students will complete their assignments before the due date.
For each student, there are only two possible outcomes, either they complete the assignment, or they do not. The probability of a student completing the assignment is independent of any other student, hence the binomial distribution is used to solve this question.
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
In this problem:
The probability is:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.65)^{8}.(0.35)^{2} = 0.1757[/tex]
[tex]P(X = 9) = C_{10,9}.(0.65)^{9}.(0.35)^{1} = 0.0725[/tex]
[tex]P(X = 10) = C_{10,10}.(0.65)^{10}.(0.35)^{0} = 0.0135[/tex]
Then:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1757 + 0.0725 + 0.0135 = 0.2617[/tex]
0.2617 = 26.17% probability that at least 8 but at most 10 students will complete their assignments before the due date.
More can be learned about the binomial distribution at https://brainly.com/question/14424710