Food Consumption at Dinner: Consider a population with mean consumption at dinner 160 gms. and standard deviation of 40

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Food Consumption at Dinner:
Consider a population with mean consumption at dinner 160 gms. and
standard
deviation of 40 gms. Nothing is known regarding the distribution of
consumption.
(a) Minimum what percentage of this population consume less than
200 gms. at
dinner?
(b) You are inviting k persons from this population for dinner. You
want probability
of shortage of food to be at most ps. Determine the minimum (in
multiple of
100 gms.) amount of food to be served in each of the following
cases.
i. k = 1, ps = 10%,
ii. k = 16 (16 is a small number), ps = 5%, and,
iii. k = 400 (400 is a large number), ps = 2%.
State your assumption and thought process.