A group of scientists wanted to study how the COVID virus might affect the oxygen saturation level, which is a number between 0 and 100. A normal oxgen saturation level is at least 95. The scientists recruited a sample of 16 COVID patients who were at least 65 years old (Sample A), and measured the oxygen saturation level of the patients. The data are listed below.

Sample A: 92.9, 91.3, 93.3, 93.1, 92.7, 92.8, 91.4, 93.7, 93.7, 91.6, 91.8, 92.5, 91.3, 92.0, 92.0, 92.3

(a) (4 points) In this question, we assume that the data in Sample A were drawn from a normal distribution with mean 92 and variance 1 identically and independently. Let xA denote the sample mean of Sample A. Describe the sampling distribution of xA and use the 3- rule to show that P(xA > 93) < 1%.