On the planet of Mercury, $4-$year$-$olds average $3$ hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is $1\mathrm{.}4$ hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian $4-$year$-$old living in a rural area. We are interested in the amount of time X the child spends alone per day. $($Source: San Jose Mercury News$)$ Round all answers to $4$ decimal places where possible.

a$.$  What is the distribution of X$?$ X ~ N$(,)$

b$.$  Find the probability that the child spends less than $1$ hours per day unsupervised.

c$.$  What percent of the children spend over $3\mathrm{.}8$ hours per day unsupervised. $\%($Round to $2$ decimal places$)$

d$.88\%$ of all children spend at least how many hours per day unsupervised? hours.