please answer q:5 and 6

5. The volume (in fluid ounces) placed in a bottle by a bottling machine follows a normal distribution with mean a and variance o'. Over a long period of time, it is observed that 5% of the bottles contain less than 31.5 ounces, while 15% contain more than 32.3 ounces. [6] (a) Find p and a. [2] (b) What proportion of the bottles contain more than 32.2 ounces? [2] (c) We observe bottles until we find 3 with more than 32.2 ounces. What is the probability that 10 bottles must be observed in total? 6. Suppose X and Y are independent random variables with X ~ N(3, 4) and Y ~ N(-8, 25). Let U = X -5Y and V = -6X +cY, where c is a constant. [3] (a) What are the distributions of U and V? (3) (b) Find the value of b such that P(U 0.5