A parabolic satellite dish reflects signals to the dish's focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function f(x) = c ( l -1/16x² ) for 0 < x < 2, where x is the distance (in meters) from the centroid of the dish surface to a reflection point at which a signal arrives. Determine the 16 following: Round your answers to two decimal places (e.g. 98.76).)

Value of c that makes f (x) a valid probability density function

c = ______________