According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for non‑Hispanic black males was
71.8
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.

Let
¯¯¯
x
be the mean life expectancy in a sample of
100
non‑Hispanic black males. Determine the interval centered at the population mean
μ
such that
95
%
of sample means
¯¯¯
x
will fall in the interval. Give your answers precise to one decimal.