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? statistics calculator

Explanation:

Step1: Recall Normal Distribution Properties

In a normal distribution, the data is symmetric about the mean. The mean ($\mu$) is 75 seconds, and we want the percentage of times faster than 75 seconds (i.e., less than 75 seconds, since faster means a lower time).

Step2: Symmetry of Normal Curve

The normal distribution is symmetric around the mean, so the area to the left of the mean (where values are less than the mean) is equal to the area to the right of the mean (where values are greater than the mean). The total area under the normal curve is 1 (or 100% when expressed as a percentage). Since the distribution is symmetric, the area to the left of the mean ($\mu$) is $\frac{1}{2}$ (or 50%) of the total area.

Answer:

50.0%