Answer to Question #323854 in Statistics and Probability for Bless

Question

 Suppose that all athletes run 200 metres and the time they take to run is normally distributed with mean 12 seconds and a standard deviation of 3 seconds. The coach has decided that 40 percent of the athletes who can run the distance in the least time will be sent to participate in the Olympics. What is the cutoff score that will be decide which members of the time will qualify.

Answer 1

$\mu=12, \sigma=3.$

The 40th percentile of a normal distribution is $z=-0.253\text{ (find from z-table)};$

$P(Z<-0.253)=0.4;\\ z=\cfrac{x-\mu}{\sigma};\\$

$x=z\sigma+\mu=-0.253\cdot3+12=11.241$ seconds is the cutoff score.