Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 20 minutes. A researcher observed 16 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 ? T - N( c. What is the distribution of a? >x - d. If one randomly selected student is timed, find the probability that this student's time will be between 45 and 48 minutes. e. For the 16 students, find the probability that their average time studying is between 45 and 48 minutes. f. Find the probability that the randomly selected 16 students will have a total study time more than 784 minutes. g. For part e) and f), is the assumption of normal necessary? O NoO Yes h. The top 15% of the total study time for groups of 16 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

D, e, f and h

The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 60 minutes and a standard deviation of 14 minutes. Suppose one person at the hot springs is randomly chosen. Let X = the amount of time that person spent at Grover Hot Springs . Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that a randomly selected person at the hot springs stays longer then 81 minutes. c. The park service is considering offering a discount for the 7% of their patrons who spend the least time at the hot springs. What is the longest amount of time a patron can spend at the hot springs and still receive the discount? minutes. d. Find the Inter Quartile Range (IQR) for time spent at the hot springs. Q1: minutes Q3: minutes IQR: minutes

The avg. … (please complete only part c and d the rest is completed)