Question

A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course.a. Compute the probability that two or fewer will withdraw.b. Compute the probability that exactly four will withdraw.c. Compute the probability that more than three will withdraw.d. Compute the expected number of withdrawals.

Answer 1

Explanation:

Given that a university found that 20% of its students withdraw without completing the introductory statistics course.

Each student is independent of the other and there are only two outcomes

X no of students in the registered 20 is binomial with p = 0.2

a)the probability that two or fewer will withdraw.

=
`P(X\leq 2)\\=0.2061`

b. Compute the probability that exactly four will withdraw.

=
`P(X=4) = 0.2182`

c. Compute the probability that more than three will withdraw.

`=P(X>3)\\\\=1-F(2)\\= 1-0.4115\\=0.5885`

d. Compute the expected number of withdrawals.

E(x) = np = 4