The probability distribution of the discrete random variable X is given in the following:

For x = 1, 2, 3, 4, 5.

P(X=x) = 0.3, p, 0.1, q, 0.05.

(a) Show that p + q = 0·55. [1]

(b) Given that E(X) = 2·75, show that p = 0·15 and q = 0·4. [4]

(c) Find the variance of X. [3]

(d) The random variable Y is defined by Y = 4X + 2.

(i) Find the mean and variance of Y.

(ii) Find P(Y < 15). [6]

I have got all the way to the second part of (d).

for c, I calculated the variance of X to be 1.8875.

for d1] the mean was 14 and the variance was 30.2.

How is P(Y < 15) found?

It's probably something very simple. Thank you if you can steer me in the right direction as to what it is