2 Suppose XB25 070 Fill in the blank PX175 SolutionHere mea

2. Suppose X~B(25, 0.70).
Fill in the blank.

  P(X17.5) = _______

Solution

Here,

mean = u = n p = 25*0.70 = 17.5

standard deviation = sqrt(np(1-p)) = sqrt(25*0.70*(1-0.70)) = 2.291287847

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    17.5      
u = mean =    17.5      
          
s = standard deviation =    2.291287847      
          
Thus,          
          
z = (x - u) / s =    0      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   0   ) =    0.5 [ANSWER]