@ Question 2 v & 0/1 pt 3 299 @ Details The average time to run the 5K fun run is 23 minutes and the standard deviation is 2.5 minutes. 48 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( , ) , ) c. What is the distribution of Z x? Z x ~ N( , ) d. If one randomly selected runner is timed, find the probability that this runner's time will be between 23.1588 and 23.5588 minutes. b. What is the distribution of ? T ~ N( e. For the 48 runners, find the probability that their average time is between 23.1588 and 23.5588 minutes. f. Find the probability that the randomly selected 48 person team will have a total time more than 1123.2. g. For part e) and f), is the assumption of normal necessary? O YesO No h. The top 20% of all 48 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 @ Question 3 v 0/ pt O3 299 Details Each sweat shop worker at a computer factory can put together 4.2 computers per hour on average with a standard deviation of 0.9 computers. 40 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 Z? Z ~ N( , ) c. What is the distribution of Z r? Z T ~ N( . ) d. If one randomly selected worker is observed, find the probability that this worker will put h Hint: together between 4.1 and 4.2 computers per hour. . For the 40 workers, find the probability that their average number of computers put together per hour is between 4.1 and 4.2. Find the probability that a 40 person shift will put together between 160 and 164 computers per hour. . 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 40 workers who have the top 15% productivity. What is the least total number of computers produced by a group that receives a sticker? computers (round to the nearest computer) @ Question 4 v 21.7955) = d. Find the 76th percentile for the mean score for this sample size. e. P(20.3955