17. Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 36 seconds. If a man's running time puts him in the upper quartile of running times, that man is:
To determine whether a man's running time puts him in the upper quartile of running times, we first need to calculate the value corresponding to the upper quartile.
The upper quartile is the value that divides the data set into the top 25% and the bottom 75%. In a normal distribution, the z-score can be used to find the corresponding value.
To calculate the z-score, we can use the formula:
z = (x - μ) / σ
Where:
x = the value we want to find the z-score for
μ = the mean of the distribution
σ = the standard deviation of the distribution
For the upper quartile, we can use the fact that the 75th percentile corresponds to z = 0.6745 (assuming a standard normal distribution).
Using the given information:
μ = 93 seconds (mean)
σ = 36 seconds (standard deviation)
z = 0.6745 (z-score for the upper quartile)
Now, we can rearrange the formula to solve for x:
x = μ + z * σ
Plugging in the values:
x = 93 + 0.6745 * 36
Calculating this expression will give us the value that corresponds to the upper quartile.
You can play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html