Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 17 days and a standard deviation of 5 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 19 and 23 days. ___________

d. 65% of all of these types of trials are completed within how many days? (Please enter a whole number) _________