The length of time (in years) until a particular radioactive particle decays is a random variable t with probability density function defined by f(t)=5e5t for t in [0,00). Find (a) the mean of the distribution, (b) the standard deviation of the distribution, and (c) the probability that the random variable is between the mean and the 1 standard deviation above. (a) The mean of the distribution is years. (Round to two decimal places as needed.) (b) The standard deviation of the distribution is years. (Round to two decimal places as needed.) (c) Set up the integral necessary to find the probability that a random variable is between the mean and 1 standard deviation above the mean. dt What is the probability that a random variable is between the mean and 1 standard deviation above the mean? The probability is. (Round to four decimal places as needed.)