Question

2. The probability of getting a A in physics 0.74. Assume you randomly select 20 students enrolled In physics

a. What is the probability that exactly 14.8 students receive an A in the course.(12pts)





b. What is the probability that the fourth student you select is the first to receive an A in the course







c. What is the probability that exactly 4 students receive an A in the course. (6pts)

Answer 1

here this is binomial with parameter n=20 and p=0.74

a)(if this is 14.8 ; then probability should be 0, since it is not interger and student number can be only interger

if it is 14:

P(X=14)=

(20C14)0.7414(1−0.74)(20-14)    =

0.1768

if it is 8:

P(X=8)=

(20C8)0.748(1−0.74)(20-8)    =

0.0011

b)

  P(4th student is first to receive an A) =P(first 3 not receive an A and 4th one gets)

=(1-0.74)^3*0.74

=0.0130

c)

probability that exactly 4 students receive an A in the course :

P(X=4)=

(20C4)0.744(1−0.74)(20-4)    =

0.0000006