III Calculation (15 points) A box of nine gloves contains two left-handed gloves and seven right-handed gloves. a. If two gloves are randomly selected from the box, without replacement (the first glove is not returned to the box after it is selected), what is the probability that both gloves selected will be right-handed? b. If three gloves are selected, with replacement (the gloves are returned to the box after they are selected), what is the probability that all three will be left-handed? IV Calculation (15 points) A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8. a. What is the probability that a student scored below 91 on this exam? b. What is the probability that a student scored between 65 and 89? c. The probability is 5% that a student taking the test scores higher than what grade? d. If the professor grades on a curve (i.e., gives A's to the top 10% of the class, regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam, where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain.