Thank you for the repost

For part(i), can we assume that P(pays<0.90) is independent from P(buys pack of 3 bananas)?

Or do we have to prove that these two events are independent?

For part(iii), if the qn ask for more than one assumption made, apart from the assumption that bananas chosen to be packed in bags of 3 or 4 are independent what other assumptions can be made?

For part(i), if the mean is symmetrical(0.5), does it always mean that the mean is equals to the constant?
Eg. P(C3<0.9) = 0.5
μ = 0.9

Eg. P(C3>0.9) =0.5
μ = 0.9

For part(iv), why do we round up the expected bags of bananas instead of rounding it down?

Q1) no need to prove independent events.
Q2) other assumption: The mass of one banana is independent of one another.
Q3) P(C3<0.9)= P(C3>0.9)= 0.5, as long as the probability is 0.5, then it is symmetrical at the mean, so the miu of C3 is 0.9.
Q4) some answers use 3s.f., some use integer (as n is number of bags). You confirm with your teacher if answer is an integer or 3sf. Why not round down? It is not like finding the least or greatest n (eg n<= 16.67, greatest n= 16) , it is to find the n, so do the proper rounding to find the nearest integer to that decimal.