I appreciate your help One fitness test for high school boys is the mile run. Th

Question

I appreciate your help

One fitness test for high school boys is the mile run. The times for all high school boys are approximately normally distributed with mean 450 seconds (seven and a half minutes) and standard deviation 40 seconds. Determine the following probabilities A randomly sampled school boy will run the mile slower than 8 minutes. A randomly sampled school boy will run the mile faster than 6 minutes. Three independently random sampled persons will all run between 5 and 9 minutes. A physical-fitness association wants to designate the fastest 10% as "excellent". What time should the association set for this criteria?

Explanation / Answer

a) mean= 450

      X= 8*60 = 480

      Z = (480 - 450) / 40

          = 0.75

      P(Z < 0.75) = 0.7734

b) P(X>6)

   X= 6*60 = 360

      Z = (360 - 450) / 40

          = -90 / 40

          = -2.25

P(Z>-2.25) = 1 - .0122

                    = 0.9878

c) P( 5<X<9)

     X=5*60=300

   Z = (300-450)/40

     = -150 / 40 = -3.75

   When X=9*60 = 540

    Z =( 540 - 450) / 40

       = 90 /40 = 2.25

P( -3.25 < Z < 2.25 ) = 0.9878 - 0.0003

                                       =0.9875

d) For 10% excellent :

   z = 1.29

   1.29 = (X - 450) / 40

   X = 501.6

   For 10% excellent it should be more than 8.36 minutes   

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