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 470 seconds and a standard deviation of 60 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) 568.7 seconds
B) 393.2 seconds
C) 371.3 seconds
D) 546.8 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. Using the Z-score table, the Z-score for the 10th percentile is approximately -1.28. Using the formula: X = μ + Zσ, where μ = 470 and σ = 60, we get X = 470 + (-1.28)(60) = 393.2 seconds.

A Physical Fitness Association Is Including the Mile Run in Its