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 40 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) 408.8 seconds
B) 511.2 seconds
C) 525.8 seconds
D) 394.2 seconds

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 460 seconds and a standard deviation of 40 seconds. Using a standard normal distribution table or calculator, the z-score for the 10th percentile is approximately -1.28. Using the formula: X = μ + zσ, we get X = 460 + (-1.28)(40) = 408.8 seconds.

A Physical Fitness Association Is Including the Mile Run in Its