applied reseach

Question

1. A researcher found that the length of time for five-person student groups to reach a consensus on a sexual harassment policy at the University of Ghana has a normal distribution with mean = 2.2 hours and = 0.25. (a) What is the probability that a randomly selected group of students will reach a consensus on a similar policy in less than 1.5 hours? (b) In another experiment with a group of five students, they reached a consensus on the policy option in 1.5 hours. Would you suspect that the group had discussed the policy beforehand? Give reasons for your answer.

Answer 1

μ = 2.2 hours

σ = 0.25 hours

We need to use the z-score formula to find the probability: z = (X - μ) / σ

a.) z = (1.5 - 2.2) / 0.25 = -2.8 ⇒ P(z < -2.8) = 0.0026

The probability that a randomly selected group of students will reach a consensus on a similar policy in less than 1.5 hours is about 0.0026.

b.) Since the probability of reaching a consensus in 1.5 hours is very low (0.0026), it is reasonable to suspect that the group had discussed the policy beforehand.