A sociologists has been studying criminal justice system in large metropolitan city. She has found that throughout a five year study that the mean time between the person being arrested as well as their trial is normally distributed with the mean of 190 days and a standard deviation of 18 days.
Part A: Based upon the above information, determine the probability that a randomly selected person will go to trial less than 179 days after they are arrested? Show the graph of the standard normal distribution. Use 4 decimal places for final answer.
Part B: Also based on the above information, what is the probability that a randomly selected person will have to wait between 175 and 223 days before they go to trial? Show the graph of the standard normal distribution. Use 4 decimal places for your final answer.