Question

Suppose a high school teacher administers a 5 question true/false quiz to their students. Assume each student is independent, and is equally able to complete the quiz in any amount of time. The students have 10 minutes to complete the quiz.

a) [2 marks] What is the probability that a student takes less than 8 minutes to complete the quiz?

b) [2 marks] What is the probability that a student takes more than 5 minutes to complete the quiz?

c) [1 mark] What is the probability that a student takes less than 10 minutes to complete the quiz?

Answer 1

As, the student is equally able to complete the quiz in any amount of time, we can assume that the random variable T to complete the test follows Exponential distribution with rate = 5 questions per 10 minutes = 0.5 per minute. That is, T ~ Exponential( = 0.5)

a)

Probability that a student takes less than 8 minutes to complete the quiz = P(T < 8)

= 1 - exp(-8 * 0.5) = 0.9817

b)

Probability that a student takes more than 5 minutes to complete the quiz = P(T > 5)

= exp(-5 * 0.5) = 0.082

c)

Probability that a student takes less than 10 minutes to complete the quiz = P(T < 10)

= 1 - exp(-10 * 0.5) = 0.9933