The time t (in minutes) spent at a driver's license renewal center is exponentially distributed with a mean of 35 minutes. Exercise (a) Find the probability density function of the random variable t. The exponential probability density function f(t) = ae^-at has the mean mu = which means that a =. Exercise (b) Find the probability that t is within one standard deviation of the mean. To find the probability that t is within one standard deviation of the mean, we need to calculate P(mu - sigma