A census collected data on everyone that lived in a certain small town. The random variable $x$ is the number of girls out of four children born to a randomly selected couple in that town. Its probability distribution is shown below. Complete parts a through $c.$

$\backslash$table$[[x,0,1,2,3,4],[P(x=x),0\mathrm{.}1189,0\mathrm{.}1887,0\mathrm{.}3984,0\mathrm{.}1542,0\mathrm{.}1398]]$

a$.$ Find and interpret the mean of the random variable.

${}_x=($Round to four decimal places as needed.$)$

Interpret the mean. Choose the correct answer below.

A$.$ The observed value of the random variable will be equal to the mean of the random variable in most observations.

B$.$ As the number of observations, $n,$ decreases, the mean of the observations will approach the mean of the random variable.

C$.$ As the number of observations, $n,$ increases, the mean of the observations will approach the mean of the random variable.

D$.$ The observed value of the random variable will be less than the mean of the random variable in most observations.

b$.$ Obtain the standard deviation of the random variable.

${}_x=($Round to four decimal places as needed.$)$

c$.$ Draw a probability histogram for the random variable. Choose the correct graph below.

A$.$

B$.$

c$.$

D$.$