Question 5 [10 points} Saved You are recruiting 24 spacetravellers to populate a new planet many light years away. The travellers will need to be cryogenically frozen and to fit in the cryogenic pods they will need to be between 160cm and 202cm tall. El. d. [2 marks] Amongst the species to which you belong height can be approximated by a normal distribution with mean 126 cm and standard deviation 8cm. What is the probability that a randomly selected potential traveller will fall within the permitted height range? _ [2 marks] What is the probability that a randomly selected group of 24 travellers will all be within the permitted height range? _ [2 marks] The maximum total weight of the 24 travellers must not exceed lBDDkg meaning that their average weight should not be above 25kg. If individuals' weight is described by a normal distribution with mean 21kg and standard deviation 8kg what is the distribution of the mean weight of a sample of 24? [2 marks] What is the probability that a randomly chosen group of 24 travellers is underneath the weight limit? _ [2 marks] A colleague of yours suggests that to get the overall probability of a group of 24 travellers meeting both the height and weight constraints you should multiply the probability in {b} with the probability in {cl}. Do you agree? Why or why not