Directions: 1) Answer each part completely. Show all work and clearly indicate your final answer. You will be graded not only on your final answer, but also the quality and correctness of the work leading to it. 2) Solve the problems on your own papers. Once you have finished writing your solutions, scan the papers with your solutions into a single PDF file. Upload the PDF file you have created into Blackboard by clicking on the assignment link. The following function is called a Gaussian Function. Gaussian functions are used in statistics, image processing, signal processing, and in mathematics to solve heat and diffusion equations. - (x -b ) z f(x) = ae 2c2 Find the first and second derivative of the given Gaussian function when a = 4, b = -1, and c = 1 f' (x) = f" (z) =3-50. The reaction time of a driver to visual stimulus is nor- mally distributed with a mean of 0.4 second and a standard deviation of 0.05 second. (a) What is the probability that a reaction requires more than 0.5 second? (b) What is the probability that a reaction requires between 0.4 and 0.5 second? (c) What is the reaction time that is exceeded 90% of the time