Step 1 :The problem provides the parameters for a binomial distribution: n=35 and p=0.85.
Step 2 :The mean of a binomial distribution is calculated using the formula \(\mu = np\). Substituting the given values, we get \(\mu = 35 \times 0.85 = 29.75\).
Step 3 :The standard deviation of a binomial distribution is calculated using the formula \(\sigma = \sqrt{np(1-p)}\). Substituting the given values, we get \(\sigma = \sqrt{35 \times 0.85 \times (1-0.85)} = 2.112463017427761\).
Step 4 :Rounding the standard deviation to four decimal places, we get \(\sigma = 2.1125\).
Step 5 :Final Answer: The mean is \(\boxed{29.75}\) and the standard deviation is \(\boxed{2.1125}\).