1. a) The speed of vehicles passing on a bridge follows a normal distribution with a mean of  65 mph and a standard deviation of 8mph. Find the probability that a randomly selected  vehicle will have a speed of more than 72 miles per hour [4]  b) 65% of the vehicles have a speed of less than x mph. Find the value of x. [4]  PLEASE SHOW ALL WORKING AND EACH STEP IN COMPLETING EACH QUESTION.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.