**Problem: 5K Fun Run and Normal Distribution**The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.4 minutes. 41 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.**Questions:**a. What is the distribution of \( X \)? \( X \sim N(\ \_\_\_\_\ ,\ \_\_\_\_\ ) \)b. What is the distribution of \( \bar{x} \)? \( \bar{x} \sim N(\ \_\_\_\_\ ,\ \_\_\_\_\ ) \)c. What is the distribution of \( \sum x \)? \( \sum x \sim N(\ \_\_\_\_\ ,\ \_\_\_\_\ ) \)d. If one randomly selected runner is timed, find the probability that this runner’s time will be between 19.5378 and 20.0378 minutes. \_\_\_\_\e. For the 41 runners, find the probability that their average time is between 19.5378 and 20.0378 minutes. \_\_\_\_\f. Find the probability that the randomly selected 41-person team will have a total time more than 795.4. \_\_\_\_\g. For part e) and f), is the assumption of normal necessary? No \_\_ Yes \_\_h. The top 20% of all 41-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**Hint: Some Helpful Videos:**- Finding the Sampling Distribution [+]- Finding a Probability Using the Central Limit Theorem [+]- Finding Value Given a Probability Using the Central Limit Theorem [+]- The Central Limit Theorem for Sums [+][Submit Question]

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The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.4 minutes. 41 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( b. What is the distribution of ? - N( c. What is the distribution of a? x - N(