The pH level, a measure of acidity, is important in studies of acid rain. For a certain Florida lake, baseline measurements of acidity are made so that any changes caused by acid rain can be noted. The pH for water samples from the lake is a random variable X, with probability density function. a) Find the value of k and sketch the graph of f(x). b) Find the cumulative distribution function of pH for water samples from the lake. c) Find the probability that pH for water samples from this lake will be less than 5.5, given that it is known to be less than 6.