The average time it takes to run a course is 332 minutes wit

The average time it takes to run a course is 33.2 minutes with a standard deviation of 4.9 minutes. The association decides that only the fastest 14% runners who finish the race will receive a complimentary running suit. Assuming the times are normally distributed, determine the interval of times for prize winners.

Need step by step explanation

Solution

Normal Distribution
Mean ( u ) =33.2
Standard Deviation ( sd )=4.9
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P ( Z > x ) = 0.14
Value of z to the cumulative probability of 0.14 from normal table is 1.08
P( x-u/ (s.d) > x - 33.2/4.9) = 0.14
That is, ( x - 33.2/4.9) = 1.08
--> x = 1.08 * 4.9+33.2 = 38.492