A single die is rolled 19 times. What is the probability that a six is rolled exactly once, if it is known that at least one six is rolled? Suppose we are given a probability distribution that has a mean if 14 and a standard deviation of 0.2. Use the Chebyshev inequality to find a lower bound estimate of the following probabilities: (a) The probability that the outcome will lie between 12 and 16 (b) The probability that the outcome lies between 12.5 to 15.5 .