Question: Ms. Hall gave her class a 10-question multiple-choice quiz. Let X = the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student's grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5 and then add 50. Let G = the grade of a randomly chosen student in the class.
Easy quiz
(a) Find the mean of G. Show your method.
(b) Find the standard deviation of G. Show your method.
(c) How do the variance of X and the variance of G compare? Justify your answer.