Question

The time needed to complete a statistics test at national level is normally distributed with a mean of 120 minutes (2 hours) and standard deviation of 21 minutes.

1. What is the probability that a student complete a test between two hours (120min) and two hours and half (150min)
2. What is the probability that a student completes a stats test in more than 2 hours?

Answer 1

Let X be time needed to complete a statistics test at national level.

X is normally distributed with a mean (µ) = 120 minutes (2 hours) and standard deviation (σ) = 21 minutes.

1. Now we want to find the probability that a student completes a test between two hours (120min) and two hours and half (150min)

P(120 < X < 150) = P((120 – 120)/21 < (X - µ)/ σ <(150 - 120)/21)

                              = P(0 < Z < 1.43)

                              = P(Z ≤ 1.43) – P(Z ≤ 0)

                              = 0.9236 – 0.5 …… (Using statistical table)

                              = 0.4236

P(120 <X < 150) = 0.4236

The probability that a student completes a test between two hours (120min) and two hours and half (150min) is 0.4236.

2. Now we want to find the probability that a student completes a stats test in more than 2 hours.

We will solve this problem by standardising.

P( X > 120) = (X - µ)/ σ > (120 - 120)/21

                              = P(Z > 0)

                              = 1 - P(Z ≤ 0)

                              = 1 – 0.5…… (Using statistical table)

                              = 0.5

The probability that a student completes a stats test in more than 2 hours is 0.5