Question

When Aiden runs the 400 meter dash, his finishing times are normally distributed with a mean of 75 seconds and a standard deviation of 1 second. What percentage of races will his finishing time be faster than 75 seconds, to the nearest tenth?

Answer 1

Since his finishing times are normally distributed, we can use the z-score formula to calculate the percentage of races where his finishing time will be faster than 75 seconds.

First, we calculate the z-score for a finishing time of 75 seconds:
z = (x - μ) / σ
z = (75 - 75) / 1
z = 0

Next, we find the percentage of races where his finishing time will be faster than 75 seconds by looking up the z-score in a standard normal distribution table. A z-score of 0 corresponds to a cumulative probability of 0.500.

Therefore, 50% of races will have a finishing time faster than 75 seconds.