Question

A local university reports that 3% of its students take their general education courses on a pass/fail basis. Assume that 50 students are registered for a general education course.

a. Define the random variable in words for this experiment.

b. What is the expected number of students who have registered on a pass/fail basis?

c. What is the probability that exactly 5 are registered on a pass/fail basis?

d. What is the probability that more than 3 are registered on a pass/fail basis?

e. What is the probability that less than 4 are registered on a pass/fail basis?

Answer 1

a.

The random variable is number of students out of 50 students take their general education courses on a pass/fail basis.

b.

X ~ Binomial(n = 50, p = 0.03)

Expected number of students who have registered on a pass/fail basis = np

= 50 * 0.03

= 1.5

c.

Probability that exactly 5 are registered on a pass/fail basis = P(X = 5)

= 0.01307

d.

Probability that more than 3 are registered on a pass/fail basis = P(X > 3)

= 1 - P(X 3)

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

= 1 -  0.2180654 - 0.3372145 - 0.2555182 - 0.1264420

= 0.06276

e.

Probability that less than 4 are registered on a pass/fail basis = P(X < 4) = P(X 3)

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

= 0.2180654 + 0.3372145 + 0.2555182+  0.1264420

= 0.9372401