Suppose x, y, and z are random variables with the joint density function f(x, y, z) = ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z ≥ 0, and f(x, y, z) = 0 otherwise. (a) find the value of the constant c. (b) find p(x ≤ 1.375 , y ≤ 1.5). (round answer to five decimal places). (c) find p(x ≤ 1.375 , y ≤ 1.5 , z ≤ 1). (round answer to six decimal places).

An office supply company conducted a survey before marketing a new paper shredder designed for home use. in the survey, 80 % of the people who tried the shredder were satisfied with it. because of this high satisfaction rate, the company decided to market the new shredder. assume that 80 % of all people are satisfied with this shredder. during a certain month, 100 customers bought this shredder. find the probability that of these 100 customers, the number who are satisfied is 69 or fewer.