A garden shop sells polyanthus plants in boxes, each box containing the same number of plants. The number of plants per box which produce yellow flowers has a binomial distribution with mean 11 and variance 4.95.
(a) Find the number of plants per box.
(b) Find the probability that a box contains exactly 12 plants which produce yellow flowers.
Another garden shop sells polyanthus plants in boxes of 100 . The shop's advertisement states that the probability of any polyanthus plant producing a pink flower is 0.3 . Use a suitable approximation to find the probability that a box contains fewer than 35 plants which produce pink flowers.