Suppose that for certain microRNA of size 20 the probability of a purine is binomially distributed with probability 0.7. Say there are 100 such microRNAs, each independent of the other. Let Y denote the average number of purine in these microRNAs. Find the probability that Y is great than 15. Please give a theoretical calculation, do NOT use Monte Carlo simulation to approximate.

Using only R

Show all the steps and formulas in your calculation.