find the probability that 200 tosses of a fair die we will o

find the probability that 200 tosses of a fair die we will obtain at most 30 fives

n=200

p=1/6=0.1667

normal approximation to binomial used

Expectation = np = 33.34

Variance = np(1 - p) = 27.782222

Standard deviation = 5.2709

For at most 30 ,With correction factor, we consider 30.5

Z value for 30.5, z=(30.5-33.34)/5.2709 = -0.54

P(at most 30 fives)

=P( z <-0.54)

= 0.2946