You are recruiting 30 space travelers to populate a new planet many light years away. The travelers will need to be cryogenically frozen and to fit in the cryogenic pods they will need to be between 170cm and 200cm tall.

1.  
2. Amongst the species to which you belong height can be approximated by a normal distribution with mean 186 cm and standard deviation 10cm. What is the probability that a randomly selected potential traveler will fall within the permitted height range?
3.  
4. What is the probability that a randomly selected group of 30 travelers will all be within the permitted height range?
5.  
6. The maximum total weight of the 30 travelers must not exceed 2100kg meaning that their average weight should not be above 70kg. If individuals' weight is described by a normal distribution with mean 72kg and standard deviation 9kg what is the distribution of the mean weight of a sample of 30?
7.  
8. What is the probability that a randomly chosen group of 30 travelers is underneath the weight limit?
9.  
10. A colleague of yours suggests that to get the overall probability of a group of 30 travelers meeting both the height and weight constraints you should multiply the probability in (b) with the probability in (d). Do you agree? Why or why not?
11.