4. A cake maker produces special mint cakes. Assume that the distribution of the weights of these cakes is normal with mean 21.5 grams and standard deviation 0.4 gram.

i) Find the probability that the weight of a randomly selected mint cake is fewer than 21 grams.

ii) Suppose that eight mint cakes are selected randomly and weighed independently. Find the probability that exactly three of these cakes will weigh fewer than 21 grams.

iii) Suppose that 50 mint cakes are packed into a bag for sale. Find the probability that a randomly selected bag will contain more than 20% of the cakes weighing fewer than 21 grams.