The finishing times of a 5K race run by competitive male runners age 15-18 are approximately normal distribution with a mean tim
e of 18 minutes and a standard deviation of 2 minutes. A particularly tough 5K race tends to take these same runners 4.5 additional minutes. To earn a completion medal in this particular 5K race, the runner must complete the race within 25 minutes.
Finishing times by competitive male runners age 15-18 for the tough 5K race are approximately normally distributed with a mean of 18 + 4.5 = 22.5 minutes and a standard deviation of 2 minutes. (Adding 4.5 minutes to each runner’s time does not affect the standard deviation of the finishing times.) Using technology: normalcdf(lower: 25, upper: 10000, mean: 22.5, SD: 2) = 0.1056, so about 10.56% of competitive male runners in the 15-18 age bracket typically do not earn a completion medal at this race. Using z-scores and Table A: z = (25 – 22.5)/2 = 1.25. The area to the left of z = 1.25 is 0.8944, so the area to the right of z = 1.25 is 1 – 0.8944 = 0.1056 or 10.56%.
