According to an article, $39\%$ of adults have experienced a breakup at least once during the last $10$ years. Of nine randomly selected adults, find the probability that the number, $x,$ who have experienced a breakup at least once during the last $10$ years is

a$.$ exactly five; at most five; at least five.

b$.$ at least one; at most one.

c$.$ between four and six, inclusive.

d$.$ Determine the probability distribution of the random variable $x.$

e$.$ Strictly speaking, why is the probability distribution that you obtained in part $($d$)$ only approximately correct? What is the exact distribution called?