Chapter ?: Central Limit Theorem (Sums) E -.-"5 The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.? minutes. '9 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N|[| | 1 b. What is the distribution of if? if ~ NI[| c. What is the distribution of 23:? Zn: - N[| | |} d. If one randomly selected runner is timed, find the probabilityr that this runner's time will be between 25.05 and 25.55 minutes. | | e. _For the 9 runners, find the probability that their average time is between 25.05 and 26.35 minutes. i. :Find the probability that the randomly selected 9 person team will have a total time less than 234.9. g. For part e] and fl, is the assumption of normal necessary? [:3'Yesr-23' No h. The top 155-5\" of all 9 person team relay races will compete in the championship round. These are the 1593 lowest times. What is the longest total time that a relay team can have and still make it to the championship roundE'l minutes Chapter 7: Central Limit Theorem (Sums) '11\" '3 ans-. Each sweat shop worker at a computer factory can put together 4 computers per hour on average with a standard deviation of 0.9 computers. 9 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution. a. what is the distribution of X? X ~ NIII II Ii 1 b. What is the distribution of o? a ~ N{I c. What is the distribution of 23:? Ex N (I: II :I} d. If one randomly selected worker is observed find the probability that this worker will put together between 3.? and 4 computers per hour. I I e. For the 9 workers, find the probability tlm- number of computers put together per hour is between 3.? and 4. I I f. Find the probability that a 9 person shift will put together between 32.4 and 34.2 computers per hour. I I g. For part e] and f] is the assumption of normal necessary?'-._ 'Jhloi:J Yes h. A sticker that says "Great Dedication" will be given to the groups of 9 workers who have the top 10% productivity. What is the least total number of computers produced by a group that receives a stickerE'I Icomputers per hour [round to the nearest computer] Chapter 7: Central Limit Theorem (Sums) 0/5 13 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 22 minutes. A researcher observed 7 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 ) :? ) a - Nd d. If one randomly selected student is timed, find the probability that this student's time will be between 39 and 43 minutes. e. For the 7 students, find the probability that their average time studying is between 39 and 43 minutes. f. Find the probability that the randomly selected 7 students will have a total study time more than 259 minutes. g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 20% of the total study time for groups of 7 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