Question

At a large track meet, times in the 100-meter race follow a normal distribution with mean 11.23 seconds and standard deviation 0.46 seconds. Times in the 200-meter race follow a normal distribution with mean 20.85 seconds and standard deviation 0.87 seconds. One runner had a time of 10.67 seconds in the 100-meter race. What must his 200-meter race time be in order for him to be at the same percentile as the 100-meter race?

Answer 1

For 100-meter race,

z = (x - mean) / SD

= (10.67 - 11.23) / 0.46

= -1.22

For 200-meter race , we have to calculate x for z = -1.22

-1.22 = ( x - 20.85) / 0.87

x = 19.79