Question

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Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 18 minutes. A researcher observed 8 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X-NI b. What is the distribution of u? -N c. What is the distribution of ? --N([ d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 45 minutes e. For the 8 students, find the probability that their average time studying is between 41 and 45 minutes. f. Find the probability that the randomly selected 8 students will have a total study time more than 408 minutes. g. For parte) and f), is the assumption of normal necessary? No Yes h. The top 15% of the total study time for groups of 8 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

Answer 1

g) Yes Is right optiob

Solution :- Given n=101 P=0.9 aq=1-P=1-0.9=01 U= np=10X0.959 ronpa Vioxoxote 0-9486 a) Yes, Empherical sale tworky on it q+ 1x0.9486 is 95% one -standaod deviation is 68% = (4+ 10) [9+ [ 8.0514, 9.9486 two- standard deviation (he +20) [at ax0.9486 [ 7.1028910.8972] three-standard deviation is 99.7%. =(1+30) [9+ 3x0.9486) = [601542, 11-8458) S ए