How do i know if a package is install on my redhat machine?

giantpanda

Notice the Installed Packages in the output

$ sudo yum list coreutils-8.22-18.el7.x86_64
Loaded plugins: amazon-id, rhui-lb, search-disabled-repos
Installed Packages
coreutils.x86_64                                     8.22-18.el7                                      @anaconda/7.3

If it is not installed the output will show Available Packages

$ sudo yum list zlib.i686
Loaded plugins: amazon-id, rhui-lb, search-disabled-repos
Available Packages
zlib.i686                               1.2.7-17.el7                               rhui-REGION-rhel-server-releases