0 Question 1 v The average time to run the 5K fun run is 25 minutes and the standard deviation is 2.6 minutes. 44 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution. :FU'O . What is the distribution of X? X ~ N( , ) . What is the distribution of :3? 52 ~ N( , ) . What is the distribution of Z 9:? Z x ~ N( , ) . If one randomly selected runner is timed, find the probability that this runner's time will be between 24.612 and 25.012 minutes. . For the 44 runners, find the probability that their average time is between 24.612 and 25.012 minutes. . Find the probability that the randomly selected 44 person team will have a total time more than 1073.6. . For part e) and f), is the assumption of normal necessary? O YesO No . The top 20% of all 44 person team relay races will compete in the championship round. These are the 20% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes O Question 2 v 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. 47 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 ~ N( , ) b. What is the distribution of :E? 5% ~ N( , ) c. What is the distribution of Z 9:? Z :1: ~ N( , ) d. If one randomly selected worker is observed, find the probability that this worker will put together between 3.8 and 3.9 computers per hour. e. For the 47 workers, find the probability that their average number of computers put together per hour is between 3.8 and 3.9. f. Find the probability that a 47 person shift will put together between 183.3 and 188 computers per houn . For part e) and f), is the assumption of normal necessary? O YesO No . A sticker that says \"Great Dedication" will be given to the groups of 47 workers who have the top 10% productivity. What is the least total number of computers produced by a group that receives a 3'00 sticker? computers per hour (round to the nearest computer) 0 Question 3 v Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 49 minutes and standard deviation 20 minutes. A researcher observed 49 students who entered the library to study. Round all answers to 4 decimal places where possible. :00 . What is the distribution of X? X ~ N( , ) . What is the distribution of :E? :7: ~ N( , ) . What is the distribution of Z :13? Z :1: ~ N( , ) . If one randomly selected student is timed, find the probability that this student's time will be between 50 and 51 minutes. . For the 49 students, find the probability that their average time studying is between 50 and 51 minutes. . Find the probability that the randomly selected 49 students will have a total study time less than 2205 minutes. . For part e) and f), is the assumption of normal necessary? O YesO No . The top 20% of the total study time for groups of 49 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 0 Question 4 v The average amount of money that people spend at Don Mcalds fast food place is 57.8200 with a standard deviation of 51.8000. 49 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N( , ) b. What is the distribution of :E? :3 ~ N( , ) c. What is the distribution of 2 ac? Z :1: ~ N( , ) d. What is the probability that one randomly selected customer will spend more than 57.8644? e. For the 49 customers, find the probability that their average spent is less than 57.8644. f. Find the probability that the randomly selected 49 customers will spend more than 5385,3556. g. For part e) and f), is the assumption of normal necessary? 0 N00 Yes h. The owner of Don Mcalds gives a coupon for a free sundae to the 2% of all groups of 49 people who spend the most money. At least how much must a group of 49 spend in total to get the free sundae? $ 0 Question 5 v The average score for games played in the NFL is 22.5 and the standard deviation is 9.2 points. 46 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of :E? 5% ~ N( , ) b. What is the distribution of Z :13? :3 ~ N( , ) c. P(a': > 20.4653) = d. Find the 68th percentile for the mean score for this sample size. e. P(22.9653