10 Treat the number of months X after January 1 that someone is born as uniformly distributed from 0 to 12. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - U( b. Suppose that 38 people are surveyed. What is the distribution of I for this sample? I ~ N( c. What is the probability that the average birth month of the 38 people will be less than 6.3?9 Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 41 minutes and standard deviation 18 minutes. A researcher observed 41 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of D? C - N( C. What is the distribution of d. If one randomly selected student is timed, find the probability that this student's time will be between 38 and 39 minutes. e. For the 41 students, find the probability that their average time studying is between 38 and 39 minutes. f. Find the probability that the randomly selected 41 students will have a total study time less than 1722 minutes. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 10% of the total study time for groups of 41 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker? minutes