(t point) As reported in \"Runner\'s World magazine, the times of the finishers

Question

(t point) As reported in "Runner's World magazine, the times of the finishers in the New York Cily 10 km run are normally distributed with a mean of 61 minutles and a deviation of 9 minules. Let x denote inishing line for the finishers a) The distribution of the variable x has mean 61 b) The distribution of the standardized variable z has mean c) The 6700 d) The percentage of inishers with times exceeding 81 minutes is equal to the area under the standard normal curve and standard deviaton9 and standard deviation and e of finishers with times between 45 and 65 minutes is equal to the area under the standard normal curve of that lies to the

Explanation / Answer

a) 61 , 9
b)

Z = (X - 61)/9

0 , 1
c)

P(45 < X< 65)
= P ( 1.78<Z<0.44 )=0.6325
hence
-1.78 , 0.44

d)
P(X > 81) =
P (Z>2.22)=0.0132
right , 2.22

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