At a recent meeting at the American College of Asthma, Allergy, and Immunology, researchers reported that allergy vaccinations are effective in treating sinusitis (inflammation of the membrane lining the facial sinuses) in individuals predisposed to allergies. Specifically, the researchers reported that $98 \%$ of individuals predisposed to allergies find relief from their sinusitis after allergy vaccinations. Suppose that this number is accurate and that 130 individuals predisposed to allergies are chosen at random and given allergy vaccinations. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of individuals in the random sample who do not find relief from their sinusitis 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 a binomial distribution problem. The binomial distribution is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are labeled 'success' and 'failure'. We are asked to find the mean and standard deviation of the distribution.

Step 2 ：The mean of a binomial distribution is given by np where n is the number of trials and p is the probability of success. In this case, n = 130 (the number of individuals) and p = 0.98 (the probability of finding relief from sinusitis).

Step 3 ：The standard deviation of a binomial distribution is given by \(\sqrt{np(1-p)}\) where n is the number of trials, p is the probability of success and (1-p) is the probability of failure.

Step 4 ：Given n = 130 and p = 0.98, we can calculate the mean as \(np = 130 \times 0.98 = 127.4\)

Step 5 ：We can also calculate the standard deviation as \(\sqrt{np(1-p)} = \sqrt{130 \times 0.98 \times (1-0.98)} = 1.596\)

Step 6 ：Final Answer: The estimated number of individuals in the random sample who do not find relief from their sinusitis is \(\boxed{127.4}\) and the standard deviation of the distribution is \(\boxed{1.596}\).