Running times for 400 meters is usually distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. What percent of runners with finish after 110 minutes?
so close to zero that you couldn't tell the difference
... unless, of course, you mean seconds instead of minutes
110 seconds is one second above one standard deviation from the mean
find the z-score (number of standard deviations from the mean)
... and use a table to find the percentage
To find the percent of runners who finish after 110 seconds, we need to calculate the area under the normal distribution curve to the right of 110 seconds.
First, let's convert 110 minutes to seconds:
110 minutes * 60 seconds/minute = 6600 seconds
Now, we need to standardize the value of 6600 seconds using the z-score formula:
z = (x - mean) / standard deviation
For 6600 seconds:
z = (6600 - 93) / 16
Calculating this value gives us:
z ≈ 409.3125
Since the z-score is extremely large, we can assume it falls outside the range of what is reasonable. Therefore, the probability of runners finishing after 110 minutes is close to 0%.
In practical terms, it is highly unlikely for any runner to take more than 110 minutes to finish a 400-meter race.