The time for the first widget to be manufactured each morning is random between 1 and 3 seconds with a pdf of f(x)= 1 2786 (x−9)2(x+6) for 0 < x < 14 What is the cumulative distribution function, F(x)? 1 2786 1 4 x4+ −12 3 x3+ −27 2 x2+486x 1 2786 1 4 x4+ 486 3 x3+ −27 2 x2+−12x 1 2786 1 4 x4+ −27 3 x3+ 486 2 x2+−12x 1 2786 1 4 x4+ −27 3 x3+ −12 2 x2+486x 1 2786 1 4 x4+ 486 3 x3+ −12 2 x2+−27x 1 2786 1 4 x4+ −12 3 x3+ 486 2 x2+−27x What is the probability of a widget being made earlier than 2 s? Answer to four decimal places What is the probability of a widget being made later than 12.2 s? Answer to four decimal places