More SAMPLING problems to think upon.

i) A liquid drug is marketed in phials containing a nominal 1.5ml but the amounts can vary slightly. The volume in each phial may be modelled by a normal distribution with the mean 1.5ml and standard deviation x ml. The phials are sold in packs of 5 randomly chosen phials . It is required that in less than 0.5% of the packs will the total volume of the drug be less than 7.5ml . Find the greatest possible value of x.

ii) A goods lift can carry up to 5000 kg and is to be loaded with crates whose masses are normally distributed with mean 79.2 kg and standard deviation 5.5 kg. Show that
a) it is highly likely that the lift can take 62 randomly selected crates without being overloaded,
b) 65 randomly selected caters would almost certainly overload the lift.

Still searching..

I m myself , kind of lost in decoding these problems. I have taken them from A - Level, Statistics -2 by Steve dobbs and James miller from ch-4. Not much detailed work is available for me to make connections and proceed ahead, so thought of sharing with you all.
Try these, it's worth the time.

Kind regard's