Auniversity 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.

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 expectance 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 = 4 withdrawals.

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers