mean and normal both are nouns.

mean and normal both are adjectives.

mean is a verb but normal is not a verb.

mean (noun)	normal (noun)
an average of n numbers computed by adding some function of the numbers and dividing by some function of n	something regarded as a normative example

mean (adjective)	normal (adjective)
approximating the statistical norm or average or expected value	conforming with or constituting a norm or standard or level or type or social norm; not abnormal
characterized by malice	in accordance with scientific laws
having or showing an ignoble lack of honor or morality	being approximately average or within certain limits in e.g. intelligence and development
marked by poverty befitting a beggar	forming a right angle
(used of persons or behavior) characterized by or indicative of lack of generosity
(used of sums of money) so small in amount as to deserve contempt
of no value or worth
very good; of the highest quality

mean (verb)	normal (verb)
mean or intend to express or convey
have as a logical consequence
denote or connote
have in mind as a purpose
have a specified degree of importance
intend to refer to
destine or designate for a certain purpose