Question

A university found that 25% of its students withdraw without completing the introductory statistics course. Assume that 18 students registered for the course.

(a) Compute the probability that 2 or fewer will withdraw.

(b) Compute the probability that exactly 5 will withdraw.

(c) Compute the probability that more than 3 will withdraw.

(d) Compute the expected number of withdrawals.

Answer 1

Solution-A:

n=18

p=0.25

q=1-p=1-0.25=0.75

P(X<=2)

=P(X=0)+P(X=1)+P(X=2)

From binomial distribution

P(X=x)=ncx*p^x*q^n-x

=18c0*0.25^0*0.75^18-0+18c1*0.25^1*0.75^18-1+18c2*0.25^2*0.75^18-2

= 0.00563771+0.03382626+0.09584107

= 0.135305

0.135305

(b) Compute the probability that exactly 5 will withdraw.

P(X=5)

==18c5*0.25^5*0.75^18-5

=0.1987815

0.1987815

Solution-c:

P(X>3)

=1-P(X<=3)

=1-(P(X=0)+P(X=1)+P(X=2)+P(X=3)

=1-(0.00563771+0.03382626+0.09584107+ 0.1703841

=1- 0.3056891

= 0.6943109

0.6943109

Solution-d:

expected number of withdrawals=np=18*0.25=4.5

expected number of withdrawals=4.5