Answer:
a) 20.61%
b) 21.82%
c) 42.36%
d) 4 withdrawals
Step-by-step explanation:
This situation can be modeled with a binomial distribution, where p = probability of “success” (completing the course) equals 80% = 0.8 and the probability of “failure” (withdrawing) equals 0.2.
So, the probability of exactly k withdrawals in 20 cases is given by
a)
We are looking for
P(0;20)+P(0;1)+P(0;2) =
0.0115292150460685 + 0.0576460752303424 + 0.136909428672063 = 0.206084718948474≅ 0.2061 or 20.61%
b)
Here we want P(20;4)
c)
Here we need
But we already have P(0;20)+P(0;1)+P(0;2) =0.2061 and
d)
For a binomial distribution the <em>expectance </em>of “succeses” in n trials is np where p is the probability of “succes”, and the expectance of “failures” is nq, so the expectance for withdrawals in 20 students is 20*0.2 = <em>4 withdrawals.</em>