Please help me as I am stuck and cannot solve these questions. Solve it as best you can if you know how to use R with clear explanations.

Link to textbook if needed with the content: https://drive.google.com/file/d/1gFvFKsvr1KJhUkz08rn9nCPwalqvc_SI/view?usp=sharing

Questions:

Question (Do the calculations by hand and use R to get the values of z or probability) The times of the finishers in the New York City 10km run are normally distributed with mean of u minutes and standard deviation 9 minutes. It is known that 80% of finishers have a finish time greater than 53.44 minutes. Let X denote the finishing time for finishers in this race. Note: You can use the functions pnorm() or qnorm() in R to help you in solving the following parts, do not use tables. The function pnorm(), compute probabilities from known bounding values. The function qnorm() , aims to do the opposite: given an area, find the boundary value that determines this area.a) Find the mean finishing time (H). Note: Show/Provide the R code that you used and output for the z-value or finding area under the standard normal curve (Copy/Paste in the word document).b) In 2013 approximately 7748 individuals took part in the run. A random sample of 20 individuals is drawn and their finishing times are recorded. Assuming everyone finished the run. What is the probability that among the 20 finishers selected their average finishing time is greater than 55 minutes. Note: Show/Provide the R code that you used and output for the z-value or finding area under the standard normal curve (Copy/Paste in the word document).c) A second, independent sample of individuals is drawn from this population. How large of a sample must be drawn if the probability that the average finishing time is less than 59 must be 30%? Note: Show/Provide the R code that you used and output for the z-value or for finding area under the standard normal curve (Copy/Paste in the word document)