Running times for 400 meters are Normally distributed for yo

Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age with a mean of 93 seconds and a standard deviation of 16 seconds. How fast does a man have to run to be in the top 1% of runners?

a. 130.2 seconds

b. 51.8 seconds

c. 134.2 seconds

d. 55.8 seconds

Solution

P ( Z > x ) = 0.01
Value of z to the cumulative probability of 0.01 from normal table is 2.33
P( x-u/ (s.d) > x - 93/16) = 0.01
That is, ( x - 93/16) = 2.33
--> x = 2.33 * 16+93 = 130.2 seconds