Use the normal distribution to approximate the desired proba

Use the normal distribution to approximate the desired probability. Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives.

Solution

We first get the z score for the critical value:          
          
x = critical value =    30.5      
u = mean = np =    33.33333333      
          
s = standard deviation = sqrt(np(1-p)) =    5.270462767      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -0.537587202      
          
Thus, the left tailed area is          
          
P(z <   -0.537587202   ) =    0.295431034 [ANSWER]