Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 19 days and a standard deviation of 4 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.

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

b. If one of the trials is randomly chosen, find the probability that it lasted at least 18 days.

c. If one of the trials is randomly chosen, find the probability that it lasted between 18 and 23 days.