Find the probability that In 200 losses of a fair sixsided d

Find the probability that In 200 losses of a fair six-sided dle. a five will be obtained at least 40 times. 0.1210 0.3875 0.8810 0.0871

Solution

We first get the z score for the critical value:          
          
x = critical value =    39.5      
u = mean = np =    33.33333333      
          
s = standard deviation = sqrt(np(1-p)) =    5.270462767      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    1.170042734      
          
Thus, the left tailed area is          
          
P(z >   1.170042734   ) =    0.120991886 = 0.1210 [answer, A]