algebra 2 word problem

Question

Paul is looking at his track team’s times for the 5K races they’ve run this year. He finds that the values are normally distributed, with a mean of 22.5 minutes and a standard deviation of 2 minutes. From this information, he finds that 2.5% of the running times are longer than 26.5 minutes. What percent of running times are longer than 18.5 minutes?

Answer 1

If you look at a normal distribution curve, the center of the curve will be the mean, which is 22.5 minutes in this case. The Z-Score of 18.5 minutes is (18.5 - 22.5) / 2 = -2. So to find out what percent of running times are longer than 18.5 minutes, you will look at a standard normal curve and look for the amount of area that is above a Z-Score of -2. In this case it is: 0.977 or 97.7%