Attempt 2 According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for non‑Hispanic black females was 78.1 years. Assume that the standard deviation was 15 years, as suggested by the Bureau of Economic Research. The distribution of age at death, X , is not normal because it is skewed to the left. Nevertheless, the distribution of the mean, ¯¯¯ x , in all possible samples of size n is approximately normal if n is large enough, by the central limit theorem. Suppose that Esmé is a researcher for a large, for-profit hospital company. She takes a simple random sample of n = 100 non‑Hispanic black females obtained from all death records over the past year. Determine the sample mean, ¯¯¯ x , such that the probability is 99 % that the mean in Esmé's sample will be greater than ¯¯¯ x .