Question

1. The running time for videos submitted on a site in a given week is normally distributed with μ = 390 seconds and standard deviation σ = 148 seconds. If a single video is randomly selected, what is the probability that the running time of the video exceeds 6 minutes (360 seconds)?

Below is the way I did the problem. Find my mistake(s), and explain what I did wrong.

The problem wants us to find P (X > 390). So we first need to change into the standard normal distribution by computing the z-score:

The z-score is

z = 390-360/148 = 0.2027027027

Then we can go from P(X > 390) → P(Z > 0.20).
Then we must account for the ” > ” sign by doing P (Z > 0.20) = P (Z < 0.20) − 1.

Then our answer is P(X > 390) → P(Z > 0.20) = P(Z < 0.20)−1 = 0.5793−1 = −0.4207.

Note that the answer −0.4207 is wrong. There could be more than one mistake, find and explain why it is wrong.

Answer 1