Answer:
(a) Probability that 2 or fewer will withdraw is 0.2061.
(b) Probability that exactly 4 will withdraw is 0.2182.
(c) Probability that more than 3 will withdraw is 0.5886.
(d) The expected number of withdrawals is 4.
Step-by-step explanation:
We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.
Assume that 20 students registered for the course.
The above situation can be represented through binomial distribution;
where, n = number of trials (samples) taken = 20 students
r = number of success
p = probability of success which in our question is probability
that students withdraw without completing the introductory
statistics course, i.e; p = 20%
Let X = <u><em>Number of students withdraw without completing the introductory statistics course</em></u>
So, X ~ Binom(n = 20 , p = 0.20)
(a) Probability that 2 or fewer will withdraw is given by = P(X 2)
P(X 2) = P(X = 0) + P(X = 1) + P(X = 2)
=
=
= <u>0.2061</u>
(b) Probability that exactly 4 will withdraw is given by = P(X = 4)
P(X = 4) =
=
= <u>0.2182</u>
(c) Probability that more than 3 will withdraw is given by = P(X > 3)
P(X > 3) = 1 - P(X 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
=
=
= 1 - 0.4114 = <u>0.5886</u>
(d) The expected number of withdrawals is given by;
E(X) =
= = 4 withdrawals
