A machine that manufactures automobile pistons is estimated to produce a defective piston $3 \%$ of the time. Suppose that this estimate is correct and that a random sample of 80 pistons produced by this machine is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Step 1 ：The problem is asking for the mean and standard deviation of a binomial distribution. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. In this case, the production of a defective piston is considered a 'success', which occurs with probability \(p = 0.03\). The number of trials is the sample size, which is \(n = 80\).

Step 2 ：The mean (or expectation) of a binomial distribution is given by \(np\), and the standard deviation is given by \(\sqrt{np(1-p)}\).

Step 3 ：Substituting the given values into the formulas, we get \(mean = np = 80 * 0.03 = 2.4\) and \(std_dev = \sqrt{np(1-p)} = \sqrt{80 * 0.03 * (1-0.03)} = 1.525778489820852\).

Step 4 ：Rounding the standard deviation to at least three decimal places, we get \(std_dev = 1.526\).

Step 5 ：Final Answer: The mean number of defective pistons in the sample is \(\boxed{2.4}\) and the standard deviation is \(\boxed{1.526}\).