Problem 6. (4 points) In a certain class, the amount of time that students take to write the final exam is normally distributed with a mean of 91.73 minutes and a standard deviation of 13.998 minutes. Please use this information to answer the following questions and please use R (not the zteble) for any calculations. a. What is the probability that a randomly selected student will take fewer than 96.5 minut to write the nal exam? Answer: ' E Bound to at least FOUR digits after the decimal if necessary. b. At the start of the exam, the invigilator states that the maximum amount of time she can allow for students to write the final exam is 125 minutes. What is the probability that a randomly selected student will need more than this allotted time to write the final exam? Answer: a a Round to at least FOUR digits after the decimal if necessaly. c. What is the maximum amount of time a student can take to write the final exam and still be within the first 17% of students nished with the exam? Answer: 3 # minutes. Round to at least FOUR digits after the decimal if necessary. d. Suppose the z-score (standardized score) of the amount of time it takes for a student to write the final exam is given as 0.66. Which of the following statements is a correct interpretation of the meaning of this value? F' A. The amount of time it takes for this student to write the final exam is 0.66 minutes more than the amount of time it takes the average student to write the final exam 0 B. The amount of time it takes for this student to write the final exam is 0.66 times more than the amount of time it takes the average student to write the final exam 0 C. The amount of time it takes for this student to write the final exam is 0.66 standard deviations more than the amount of time it takes the average student to write the nal exam 0 D. There is not enough information provided to interpret this value preview answers