Answer:
Clay's finishing time is 1.68 standard deviation above the mean finishing time for men.
Step-by-step explanation:
In statistics, a standardized score is the number of standard deviations an observation or data point is from the mean.
Let us consider a random variable, X that follows a normal distribution, N (<em>µ</em>, <em>σ</em>²).
Then <em>Z</em> is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is,
This, <em>z</em>-score is known as the standardized score.
It is provided that the distribution of finishing time for men (say, <em>X</em>) was approximately normal with mean <em>µ</em> = 242 minutes and standard deviation <em>σ = </em>29 minutes.
The finishing time for Clay was <em>x</em> = 289 minutes.
Compute Clay's <em>z</em>-score as follows:
Thus, Clay's standardized score is 1.68.
That is, Clay's finishing time is 1.68 standard deviation above the mean finishing time for men.