at a small liberal arts college, studens can register for one to six courses. Le

Question

at a small liberal arts college, studens can register for one to six courses. Let X be the number of courses taken in the fall by a randomly selected student from this college. In a typical fall semester, 5 % take one course, 5% take two courses, 13% take three courses, 26% take four courses, 36% take five courses, and 15% take six courses. Let X be the number of courses taken in the fall by a randomly selected student from this college. In a typical fall semester, 5% take one corse, 5% take two courses, 13% take three courses, 26% take four courses, 36% take five courses, and 15% take six courses. Let X be the number of courses taken in the fall by a randomly selected studet from college.

a)Describe the probability distribution of this random variable.   

b) Find the probability that a randomly selected student takes three or fewer courses

c) Find the probability that a randomly selected student takes four or five courses

d) Find the probability that a randomly selected student takes eight courses

Explanation / Answer

let X is the number of courses taken and P(X=x) is the probability corresponding to it.

a)hence from above data; below is probability distribution of X:

b)  probability that a randomly selected student takes three or fewer courses =P(X<=3) =0.05+0.05+0.13=0.23

c) probability that a randomly selected student takes four or five courses =P(4<=X<=5) =0.26+0.36=0.62

d)probability that a randomly selected student takes eight courses =0 ; (as maximum courses taken by a student is 6)

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