Question

In the Hermosa Beach triathlon, the finishing times for the men ages 30-34 group has a mean of 4400 seconds with standard deviation 580 seconds. Suppose the distribution of finishing times are approximately normal. Find the cutoff time for the fastest 10% of athletes in the men's group. Please include which distribution and why? And what parameters used.

Answer 1

Let T be the cutoff time for the fastest 10% of male athletes

It is give that the finishing time for male athletes is normally distributed with parameters,

mean () = 4400 s

standard deviation () = 580 s

P(X < A) = P(Z < (A - )/)

P(X < T) = 0.10

P(Z < (T - 4400)/580) = 0.10

Take the z score corresponding to probability of 0.1000 from standard normal distribution table

(T - 4400)/580 = -1.28

T = 3658 seconds