Question

Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below:
x 1 2 3 4 5 6 7
p(x) .04 .05 .08 .26 .39 .16 .02
(a) What is P(x = 4)?
P(x = 4) =

(b) What is P(x 4)?
P(x 4) =

(c) What is the probability that the selected student is taking at most five courses?
P(at most 5 courses) =

(d) What is the probability that the selected student is taking at least five courses? more than five courses?
P(at least 5 courses) =
P(more than 5 courses) =

(e) Calculate P(3 x 6) and P(3 < x < 6).
P(3 x 6) =
P(3 < x < 6) =

Answer 1

Given probability distribution (pdf):
x 1 2 3 4 5 6 7
p(x) .04 .05 .08 .26 .39 .16 .02

Since &Sum;p(x) for x=1 to 7 =1.0
we conclude that:
p(0)=0
p(1)=0.04
...
p(7)=0.02
p(8+)=0
(a)
P(x=4)=0.26/1=0.26
(b)
P(x>4)
=P(5)+P(6)+P(7)+P(8+)
=0.39+0.16+0.02+0
=0.53
(c)
P(x≤5)=P(0-)+P(1)+P(2)+P(3)+P(4)+P(5)
=?

(d) P(x≥5)=P(x>4)

(e)
P(3≤x≤6)=P(3)+P(4)+P(5)+P(6)
P(3<x<6)=P(4)+P(5)

Answer 2

Fifty students are polled on the courses they are taking, and X is the number of courses a student takes. The number of courses ranges from 2 to 6. Is the following a probability distribution of X?