Use R/RStudio to solve, please include code.

4.74. Scores on an examination are assumed to be normally distributed with mean 78 and variance 36. a. What is the probability that a person taking the examination scores higher than 72'? b. Suppose that students scoring in the top 10% of this distribution are to receive an A grade. What is the minimum score a student must achieve to earn an A grade? c. What must be the cutoff point for passing the examination if the examiner wants only the top 28.1% of all scores to be passing? d. Approximately what proportion of students have scores 5 or more points above the score that cuts off the lowest 25%? e. Applet Exercise Answer parts (a). (b). (c), and (d). using the applet Norma! Tail Areas and Quantrles. f. If it is known that a student's score exceeds 72. what is the probability that his or her score exceeds 84