Question

The cdf of the random variable X is given by: x < a x — а b-0 a < x <b ( 1 x > b Let a=32 and b=79. Find the 87th percentile. Select one: a. 4121.00 O b. 32.00 c. 72.89 d. 79.00 e. 85.16

Answer 1

    CDF of X is given by              
   F(x) = 0             for x < a              

F(x) = x-a h for a <x<b

   F(x) = 1             for x > b              
   a = 32 , b = 79              

x - 32 F(x) = 70-33 for 32 sxs 79 F(x) =*132 for 32 sxs 79

    Let 87th percentile be given by X'              
    Then,
   P(X < X') = 0.87               
   Thus              

X' - 32 - 47 = 0.87

   X' = 47*0.87 + 32              
   X' = 72.89  

    Answer               
       $\mathbf{ \circ\ \ c.\ \ 72.89 }$