A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a
Mean of 460 seconds and a standard deviation of 50 seconds. The fitness association wants to
Recognize the fastest 10% of the boys with certificates of recognition. What time would the boys
Need to beat in order to earn a certificate of recognition from the fitness association?
A)377.75 seconds
B)396 seconds
C)524 seconds
D)542.25 seconds

Question

Quizplus · Accepted Answer

To find the time that corresponds to the fastest 10%, we need to find the 90th percentile of the normal distribution. Using the z-score table, the z-score for the 90th percentile is approximately 1.28. Using the formula: time = mean - (z-score * standard deviation), we get: 460 - (1.28 * 50) = 396 seconds.

A Physical Fitness Association Is Including the Mile Run in Its