A physical fitness association is including the mile run in its secondary-school fitness test. The time for thisevent for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and astandard deviation of 50 seconds. The fitness association wants to recognize the fastest 10% of the boys withcertificates of recognition. What time would the boys need to beat in order to earn a certificate of recognitionfrom the fitness association?
A) 376 sec
B) 504 sec
C) 522.25 sec
D) 357.75 sec

Question

Quizplus · Accepted Answer

To find the time that corresponds to the fastest 10%, we need to find the 10th percentile of the normal distribution with a mean of 440 seconds and a standard deviation of 50 seconds. Using the z-score table, the z-score for the 10th percentile is approximately -1.28. Using the formula: time = mean + (z-score * standard deviation), we get: time = 440 + (-1.28 * 50) = 376 seconds.

A Physical Fitness Association Is Including the Mile Run in Its