! please help ! thank you in advance!

A very expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 240 to 306 days before the birth of the child, so the pregnancy would have been less than 240 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? What is the probability that he could be the father?

a) name the random variable and what it denotes

d) what distribution does the random variable follow and why? justify your choice of distribution

e) list the parameters and their values

f) write the distribution mathematically and the possible values that the random variable can take on

g) in mathematical terms, state what we want to find and the results. what does the results mean about the context of the question?

h) list if the question is or is not about sampling distribution. if answer is about sampling distribution, list the corresponding sampling distributions and explain why

i) to find the probability by R, what is used? what is the result and what does the result mean about the context of the question