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Q:5

5. The volume (in fluid ounces) placed in a bottle by a bottling machine follows a normal distribution with mean a and variance ". 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. (a) Find p and a. (b) What proportion of the bottles contain more than 32.2 ounces? (e) 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. (a) What are the distributions of U and V? (b) Find the value of b such that P(U 0.5 1=1